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- 22:41, 21 October 2017 (diff | hist) . . (+388) . . N Coth of a sum (Created page with "==Theorem== The following formula holds: $$\coth(z_1+z_2)=\dfrac{\coth(z_1)\coth(z_2)+1}{\cosh(z_1)+\coth(z_2)},$$ where $\coth$ denotes hyperbolic cotangent. ==Proo...")
- 22:40, 21 October 2017 (diff | hist) . . (+7) . . Tanh of a sum (current)
- 22:40, 21 October 2017 (diff | hist) . . (+389) . . N Tanh of a sum (Created page with "==Theorem== The following formula holds: $$\mathrm{tanh}(z_1+z_2) = \dfrac{\tanh(z_1)+\tanh(z_2)}{1+\tanh(z_1)\tanh(z_2)},$$ where $\tanh$ denotes hyperbolic tangent....")
- 22:39, 21 October 2017 (diff | hist) . . (+7) . . Cosh of a sum (current)
- 22:38, 21 October 2017 (diff | hist) . . (+415) . . N Cosh of a sum (Created page with "==Theorem== The following formula holds: $$\cosh(z_1+z_2) = \cosh(z_1)\cosh(z_2) + \sinh(z_1)\sinh(z_2),$$ where $\cosh$ denotes hyperbolic cosine and $\sinh$ denotes...")
- 22:37, 21 October 2017 (diff | hist) . . (+416) . . N Sinh of a sum (Created page with "==Theorem== The following formula holds: $$\sinh(z_1+z_2)=\sinh(z_1)\cosh(z_2)+\cosh(z_1)\sinh(z_2),$$ where $\sinh$ denotes hyperbolic sine and $\cosh$ denotes cos...") (current)
- 22:36, 21 October 2017 (diff | hist) . . (+336) . . N Tanh is odd (Created page with "==Theorem== The following formula holds: $$\tanh(-z)=-\tanh(z),$$ where $\tanh$ denotes hyperbolic tangent. ==Proof== ==References== * {{BookReference|Handbook of m...") (current)
- 22:35, 21 October 2017 (diff | hist) . . (+331) . . N Cosh is even (Created page with "==Theorem== The following formula holds: $$\cosh(-z)=\cosh(z),$$ where $\cosh$ denotes hyperbolic cosine. ==Proof== ==References== * {{BookReference|Handbook of mat...") (current)
- 22:34, 21 October 2017 (diff | hist) . . (+6) . . Sinh is odd (current)
- 22:33, 21 October 2017 (diff | hist) . . (+44) . . Difference of cosh and sinh (current)
- 22:33, 21 October 2017 (diff | hist) . . (+341) . . N Sinh is odd (Created page with "==Theorem== The following formula holds: $$\sinh(-z)=-\sinh(z),$$ where $\sinh$ denotes hyperbolic sine. ==Proof== ==References== * {{BookReference|Handbook of math...")
- 22:32, 21 October 2017 (diff | hist) . . (+5) . . Difference of cosh and sinh
- 22:32, 21 October 2017 (diff | hist) . . (+9) . . Difference of cosh and sinh (Undo revision 8735 by Tom (talk))
- 22:31, 21 October 2017 (diff | hist) . . (-9) . . Difference of cosh and sinh
- 22:31, 21 October 2017 (diff | hist) . . (+385) . . N Difference of cosh and sinh (Created page with "==Theorem== The following formula holds: $$\cosh(z) - \sinh(z) = e^{-z},$$ where $\cosh$ denotes hyperbolic cosine, $\sinh$ denotes hyperbolic sine, and $e^{...")
- 22:30, 21 October 2017 (diff | hist) . . (+21) . . Sum of cosh and sinh (current)
- 22:29, 21 October 2017 (diff | hist) . . (+44) . . Pythagorean identity for coth and csch (current)
- 22:29, 21 October 2017 (diff | hist) . . (+449) . . N Sum of cosh and sinh (Created page with "==Theorem== The following formula holds: $$\cosh(z) + \sinh(z) = e^z,$$ where $\cosh$ denotes hyperbolic cosine, $\mathrm{sinh}$ denotes hyperbolic sine, and...")
- 22:28, 21 October 2017 (diff | hist) . . (+412) . . N Pythagorean identity for coth and csch (Created page with "==Theorem== The following formula holds: $$\mathrm{coth}^2(z)-\mathrm{csch}^2(z)=1,$$ where $\mathrm{coth}$ denotes hyperbolic cotangent and $\mathrm{csch}$ denotes [...")
- 22:26, 21 October 2017 (diff | hist) . . (+32) . . Pythagorean identity for tanh and sech (current)
- 22:25, 21 October 2017 (diff | hist) . . (+446) . . N Pythagorean identity for tanh and sech (Created page with "==Theorem== The following formula holds: $$\mathrm{tanh}^2(z)+\mathrm{sech}^2(z)=1,$$ where $\mathrm{tanh}$ denotes the hyperbolic tangent and $\mathrm{sech}$ denotes...")
- 22:25, 21 October 2017 (diff | hist) . . (+176) . . Pythagorean identity for sinh and cosh (current)
- 22:24, 21 October 2017 (diff | hist) . . (+49) . . Tanh (→Properties)
- 22:23, 21 October 2017 (diff | hist) . . (+32) . . Period of tanh (current)
- 16:07, 21 October 2017 (diff | hist) . . (+7) . . Airy Bi (current)
- 04:30, 15 September 2017 (diff | hist) . . (+39) . . Main Page (→Matrix functions)
- 03:56, 15 September 2017 (diff | hist) . . (+192) . . Main Page
- 22:10, 26 August 2017 (diff | hist) . . (+73) . . Main Page (→Special functions)
- 22:09, 26 August 2017 (diff | hist) . . (+24) . . Laplace transform
- 22:08, 26 August 2017 (diff | hist) . . (+30) . . Two-dimensional Laplace transform (current)
- 22:08, 26 August 2017 (diff | hist) . . (+444) . . N Unit step function (Created page with "The unit step function $U \colon \mathbb{R} \rightarrow \left\{ 0, \dfrac{1}{2}, 1 \right\}$ is defined by $$U(t)=\left\{ \begin{array}{ll} 0 &, \quad t<0 \\ \dfrac{1}{2}&, \q...") (current)
- 22:06, 26 August 2017 (diff | hist) . . (+414) . . N Two-dimensional Laplace transform (Created page with "The two-dimensional Laplace transform of a function $f$ is $$\mathscr{L}\{f\}(z_1,z_2)=\displaystyle\int_0^{\infty} \displaystyle\int_0^{\infty} e^{-z_1x-z_2y} \mathrm{d}x \ma...")
- 22:05, 26 August 2017 (diff | hist) . . (+27) . . Laplace transform
- 22:03, 26 August 2017 (diff | hist) . . (+50) . . Laplace transform
- 22:02, 26 August 2017 (diff | hist) . . (+2) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 22:02, 26 August 2017 (diff | hist) . . (+75) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 22:01, 26 August 2017 (diff | hist) . . (-4) . . Laplace transform
- 15:43, 11 July 2017 (diff | hist) . . (+16) . . Cosine integral (current)
- 16:11, 10 July 2017 (diff | hist) . . (+70) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 16:10, 10 July 2017 (diff | hist) . . (+134) . . Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3
- 16:10, 10 July 2017 (diff | hist) . . (+50) . . Li2(z)=zPhi(z,2,1)
- 16:09, 10 July 2017 (diff | hist) . . (+383) . . N Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (Created page with "==Theorem== The following formula holds: $$\mathrm{Li}_2(z)=-\mathrm{Li}_2 \left( \dfrac{1}{z} \right) - \dfrac{\log(z)^2}{2} + i \pi \log(z) + \dfrac{\pi^2}{3},$$ where $\mat...")
- 16:08, 10 July 2017 (diff | hist) . . (+67) . . Dilogarithm (→Properties)
- 16:03, 10 July 2017 (diff | hist) . . (-63) . . Devil's staircase (current)
- 16:03, 10 July 2017 (diff | hist) . . (+169) . . Devil's staircase
- 16:02, 10 July 2017 (diff | hist) . . (+168) . . Ramanujan theta function (current)
- 15:59, 10 July 2017 (diff | hist) . . (+28) . . Ramanujan theta function
- 15:56, 10 July 2017 (diff | hist) . . (+9) . . Debye function (current)
- 15:55, 10 July 2017 (diff | hist) . . (+36) . . Debye function
- 15:51, 10 July 2017 (diff | hist) . . (+153) . . Main Page (→Continuous nowhere-differentiable functions and friends)
- 15:51, 10 July 2017 (diff | hist) . . (-153) . . Main Page (→Special functions)
- 15:50, 10 July 2017 (diff | hist) . . (+130) . . Main Page (→Continuous nowhere-differentiable functions and friends)
- 15:50, 10 July 2017 (diff | hist) . . (-130) . . Main Page (→Special functions)
- 15:50, 10 July 2017 (diff | hist) . . (+142) . . N Devil's staircase is not absolutely continuous (Created page with "==Theorem== The Devil's staircase is not absolutely continuous. ==Proof== ==References== Category:Theorem Category:Unproven") (current)
- 15:49, 10 July 2017 (diff | hist) . . (+127) . . N Devil's staircase is continuous (Created page with "==Theorem== The Devil's staircase is continuous. ==Proof== ==References== Category:Theorem Category:Unproven") (current)
- 15:48, 10 July 2017 (diff | hist) . . (+89) . . Devil's staircase (→Videos)
- 15:47, 10 July 2017 (diff | hist) . . (+113) . . Devil's staircase
- 15:39, 10 July 2017 (diff | hist) . . (+2) . . Bessel Y (current)
- 15:39, 10 July 2017 (diff | hist) . . (+197) . . Cosecant (→Properties) (current)
- 04:49, 7 July 2017 (diff | hist) . . (+124) . . N Silver ratio (Created page with "The silver ratio $\delta_s$ is the number $$\delta_s=1+\sqrt{2}.$$ =Properties= =References= Category:SpecialFunction") (current)
- 04:47, 7 July 2017 (diff | hist) . . (+30) . . Derivative of cosine integral (current)
- 17:34, 1 July 2017 (diff | hist) . . (-1) . . Sine (current)
- 17:34, 1 July 2017 (diff | hist) . . (-13) . . Sine
- 17:30, 1 July 2017 (diff | hist) . . (-66) . . Main Page (→$q$-special functions)
- 17:10, 1 July 2017 (diff | hist) . . (0) . . Champernowne constant (current)
- 03:22, 1 July 2017 (diff | hist) . . (0) . . Upper incomplete gamma (current)
- 03:19, 1 July 2017 (diff | hist) . . (-5) . . Taylor series of sine (current)
- 03:18, 1 July 2017 (diff | hist) . . (-6) . . Taylor series of cosine (current)
- 03:09, 1 July 2017 (diff | hist) . . (0) . . Series for log(riemann zeta) over primes (current)
- 03:06, 1 July 2017 (diff | hist) . . (+12) . . Relationship between the Fransén–Robinson constant, e, pi, and logarithm (current)
- 02:17, 1 July 2017 (diff | hist) . . (0) . . Logarithmic derivative of Riemann zeta in terms of series over primes (current)
- 02:07, 1 July 2017 (diff | hist) . . (0) . . m Log a(b)=1/log b(a) (Tom moved page Log a(z)=1/log b(a) to Log a(b)=1/log b(a)) (current)
- 02:07, 1 July 2017 (diff | hist) . . (+33) . . N Log a(z)=1/log b(a) (Tom moved page Log a(z)=1/log b(a) to Log a(b)=1/log b(a)) (current)
- 02:07, 1 July 2017 (diff | hist) . . (0) . . Log a(b)=1/log b(a)
- 01:55, 1 July 2017 (diff | hist) . . (+18) . . Integral representation of Airy Ai
- 01:54, 1 July 2017 (diff | hist) . . (-15) . . Integral of log of inverse erf from 0 to 1 (current)
- 01:45, 1 July 2017 (diff | hist) . . (0) . . Gamma function written as infinite product
- 01:33, 1 July 2017 (diff | hist) . . (+1) . . Differential equation for Jacobi P (current)
- 01:31, 1 July 2017 (diff | hist) . . (0) . . Derivative of Legendre chi 2 (current)
- 01:29, 1 July 2017 (diff | hist) . . (0) . . Derivative of cotangent (→Proof) (current)
- 01:28, 1 July 2017 (diff | hist) . . (-1) . . Derivative of cotangent (→Proof)
- 01:28, 1 July 2017 (diff | hist) . . (0) . . Derivative of cotangent
- 01:27, 1 July 2017 (diff | hist) . . (0) . . Derivative of cosine (current)
- 01:16, 1 July 2017 (diff | hist) . . (+12) . . Beta in terms of power of t over power of (1+t) (current)
- 15:12, 27 June 2017 (diff | hist) . . (+80) . . Mersenne numbers (current)
- 20:35, 25 June 2017 (diff | hist) . . (+134) . . N The Petr function is continuous (Created page with "==Theorem== The Petr function is continuous on $(0,1)$. ==Proof== ==References== Category:Theorem Category:Unproven") (current)
- 20:34, 25 June 2017 (diff | hist) . . (+146) . . N The Petr function is nowhere differentiable (Created page with "==Theorem== The Petr function is nowhere differentiable on $(0,1)$. ==Proof== ==References== Category:Theorem Category:Unproven") (current)
- 20:34, 25 June 2017 (diff | hist) . . (-339) . . Petr function (→Properties) (current)
- 20:28, 25 June 2017 (diff | hist) . . (+35) . . Polylogarithm (current)
- 20:28, 25 June 2017 (diff | hist) . . (-84) . . Logarithm
- 20:28, 25 June 2017 (diff | hist) . . (+35) . . Logarithmic integral
- 20:27, 25 June 2017 (diff | hist) . . (+35) . . Dilogarithm
- 20:25, 25 June 2017 (diff | hist) . . (+586) . . N Logarithm and friends footer (Created page with "<center><strong>Logarithm and friends</strong></center> <div class="grid"> <div class="grid"><center>File:Dilogarithmthumb.png|45px|link=Dil...") (current)
- 20:25, 25 June 2017 (diff | hist) . . (-464) . . Main Page (→Logarithm function and friends)
- 20:24, 25 June 2017 (diff | hist) . . (-61) . . Jacobi theta 4 (current)
- 20:23, 25 June 2017 (diff | hist) . . (-61) . . Jacobi theta 3 (current)
- 20:23, 25 June 2017 (diff | hist) . . (-61) . . Jacobi theta 2 (current)
- 20:23, 25 June 2017 (diff | hist) . . (-62) . . Jacobi theta 1 (current)
- 20:23, 25 June 2017 (diff | hist) . . (+718) . . N Jacobi theta footer (Created page with "<center><strong>Jacobi theta functions</strong></center> <div class="grid"> <div class="grid"><center>Jacobi theta 1|<randomimagebycategory categorie...") (current)
- 20:22, 25 June 2017 (diff | hist) . . (-1) . . Main Page (→Jacobi theta functions)
- 20:22, 25 June 2017 (diff | hist) . . (-612) . . Main Page (→Jacobi theta functions)
- 20:15, 25 June 2017 (diff | hist) . . (-129) . . Logarithm
- 20:14, 25 June 2017 (diff | hist) . . (+49) . . Logarithm
- 20:14, 25 June 2017 (diff | hist) . . (+51) . . Logarithm
- 20:14, 25 June 2017 (diff | hist) . . (+61) . . Logarithm
- 20:14, 25 June 2017 (diff | hist) . . (+52) . . Logarithm
- 20:14, 25 June 2017 (diff | hist) . . (+43) . . Logarithm
- 20:13, 25 June 2017 (diff | hist) . . (+39) . . Logarithm
- 20:13, 25 June 2017 (diff | hist) . . (+38) . . Logarithm
- 20:13, 25 June 2017 (diff | hist) . . (+32) . . Logarithm
- 20:13, 25 June 2017 (diff | hist) . . (+30) . . Logarithm
- 20:12, 25 June 2017 (diff | hist) . . (+38) . . Logarithm
- 20:12, 25 June 2017 (diff | hist) . . (+32) . . Logarithm
- 20:11, 25 June 2017 (diff | hist) . . (+607) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 20:09, 25 June 2017 (diff | hist) . . (+555) . . N Log((1+z)/(1-z)) as continued fraction (Created page with "==Theorem== The following formula holds for $z \in \mathbb{C} \setminus \left[ (-\infty,-1) \bigcup (1,\infty) \right]$: $$\log \left( \dfrac{1+z}{1-z} \right) = \cfrac{2z}{1-...")
- 20:04, 25 June 2017 (diff | hist) . . (+516) . . N Log(1+z) as continued fraction (Created page with "==Theorem== The following formula holds for any $z \in \mathbb{C} \setminus (-\infty,-1)$: $$\log(1+z)=\cfrac{z}{1+\cfrac{z}{2+\cfrac{z}{3+\cfrac{4z}{4+\cfrac{4z}{5+\cfrac{9z}...") (current)
- 19:59, 25 June 2017 (diff | hist) . . (+407) . . N Abs(log(1+z)) less than or equal to -log(1-abs(z)) (Created page with "==Theorem== The following formula holds for $|z|<1$: $$\left| \log(1+z) \right| \leq - \log(1-|z|),$$ where $\log$ denotes the logarithm. ==Proof== ==References== * {{Bo...") (current)
- 19:57, 25 June 2017 (diff | hist) . . (+432) . . N Log(x) less than or equal to n(x^(1/n)-1) (Created page with "==Theorem== The following formula holds for $x>0$ and $n>0$: $$\log(x) \leq n \left( x^{\frac{1}{n}} - 1 \right),$$ where $\log$ denotes the logarithm. ==Proof== ==Refer...") (current)
- 19:56, 25 June 2017 (diff | hist) . . (+377) . . N Log(x) less than or equal to x-1 (Created page with "==Theorem== The following formula holds for $x>0$: $$\log(x) \leq x-1,$$ where $\log$ denotes the logarithm. ==Proof== ==References== * {{BookReference|Handbook of mathe...") (current)
- 19:54, 25 June 2017 (diff | hist) . . (+402) . . N Abs(log(1-x)) less than 3x/2 (Created page with "==Theorem== The following formula holds for $0<x \leq 0.5828$: $$\left| \log(1-x) \right| < \dfrac{3x}{2},$$ where $\log$ denotes the logarithm. ==Proof== ==References==...") (current)
- 19:53, 25 June 2017 (diff | hist) . . (+3) . . -log(1-x) less than x/(1-x) (current)
- 19:52, 25 June 2017 (diff | hist) . . (+378) . . N -log(1-x) less than x/(1-x) (Created page with "==Theorem== The following formula holds for $x<1$ and $x\neq 0$: $$-\log(1-x) < \dfrac{x}{1-x},$$ where $\log$ denotes the logarithm. ==Proof== ==References== * {{BookRe...")
- 19:51, 25 June 2017 (diff | hist) . . (+367) . . N X less than -log(1-x) (Created page with "==Theorem== The following formula holds for $x<1$ and $x \neq 0$: $$x < -\log(1-x),$$ where $\log$ denotes the logarithm. ==Proof== ==References== * {{BookReference|Hand...") (current)
- 19:50, 25 June 2017 (diff | hist) . . (+350) . . N Log(1+x) less than x (Created page with "==Theorem== The following formula holds for $x>-1$: $$\log(1+x)<x,$$ where $\log$ denotes the logarithm. ==Proof== ==References== * {{BookReference|Handbook of mathemati...") (current)
- 19:49, 25 June 2017 (diff | hist) . . (+363) . . N X/(1+x) less than log(1+x) (Created page with "==Theorem== The following formula holds for $x>-1$: $$\dfrac{x}{1+x} < \log(1+x),$$ where $\log$ denotes the logarithm. ==Proof== ==References== * {{BookReference|Handbo...") (current)
- 19:47, 25 June 2017 (diff | hist) . . (+8) . . Euler-Mascheroni constant
- 19:47, 25 June 2017 (diff | hist) . . (+2) . . Euler-Mascheroni constant
- 19:47, 25 June 2017 (diff | hist) . . (+161) . . Euler-Mascheroni constant
- 19:46, 25 June 2017 (diff | hist) . . (+425) . . N Limit of x^a log(x)=0 (Created page with "==Theorem== The following formula holds for $a \in \mathbb{C}$ with $\mathrm{Re}(a)>0$: $$\displaystyle\lim_{x \rightarrow 0^+} x^a \log(x)=0,$$ where $\log$ denotes the log...") (current)
- 19:43, 25 June 2017 (diff | hist) . . (+474) . . N Limit of log(x)/x^a=0 (Created page with "==Theorem== The following formula holds for $a \in \mathbb{C}$ with $\mathrm{Re}(a)>0$: $$\displaystyle\lim_{x \rightarrow \infty} \dfrac{\log(x)}{x^a} = 0,$$ where $\log$ den...") (current)
- 19:38, 25 June 2017 (diff | hist) . . (-14) . . Logarithm (→Properties)
- 19:38, 25 June 2017 (diff | hist) . . (+46) . . Logarithm
- 19:36, 25 June 2017 (diff | hist) . . (+34) . . Logarithm base a (current)
- 19:36, 25 June 2017 (diff | hist) . . (+34) . . Logarithm
- 19:36, 25 June 2017 (diff | hist) . . (+36) . . Logarithm
- 19:35, 25 June 2017 (diff | hist) . . (+36) . . E (current)
- 19:35, 25 June 2017 (diff | hist) . . (+36) . . Logarithm base a
- 19:35, 25 June 2017 (diff | hist) . . (+35) . . Logarithm
- 19:35, 25 June 2017 (diff | hist) . . (+35) . . Logarithm base a
- 19:35, 25 June 2017 (diff | hist) . . (+26) . . Logarithm
- 19:34, 25 June 2017 (diff | hist) . . (+26) . . E
- 19:34, 25 June 2017 (diff | hist) . . (+26) . . Logarithm base a
- 19:34, 25 June 2017 (diff | hist) . . (+30) . . Logarithm base a
- 19:34, 25 June 2017 (diff | hist) . . (+50) . . Logarithm base a
- 19:33, 25 June 2017 (diff | hist) . . (+27) . . Logarithm (multivalued) (current)
- 19:33, 25 June 2017 (diff | hist) . . (+27) . . Logarithm
- 19:33, 25 June 2017 (diff | hist) . . (+66) . . Logarithm base a
- 19:32, 25 June 2017 (diff | hist) . . (+1) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 19:32, 25 June 2017 (diff | hist) . . (+267) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 19:30, 25 June 2017 (diff | hist) . . (+19) . . Log(z)=log(10)log 10(z) (current)
- 19:30, 25 June 2017 (diff | hist) . . (+381) . . N Log(z)=log(10)log 10(z) (Created page with "==Theorem== The following formula holds: $$\log(z)=\log(10)\log_{10}(z),$$ where $\log$ denotes logarithm and $\log_{10}$ denotes logarithm base a. ==Proof== ==Refer...")
- 19:29, 25 June 2017 (diff | hist) . . (+421) . . N Log 10(z)=log 10(e)log(z) (Created page with "==Theorem== The following formula holds: $$\log_{10}(z)=\log_{10}(e)\log(z),$$ where $\log_{10}$ denotes logarithm base a, $e$ denotes e, and $\log$ denotes logarith...") (current)
- 19:27, 25 June 2017 (diff | hist) . . (+19) . . Log 10(z)=log(z)/log(10) (current)
- 19:27, 25 June 2017 (diff | hist) . . (+380) . . N Log 10(z)=log(z)/log(10) (Created page with "==Theorem== The following formula holds: $$\log_{10}(z)=\dfrac{\log(z)}{\log(10)},$$ where $\log_{10}$ denote logarithm base a and $\log$ denotes logarithm. ==Proof==...")
- 19:26, 25 June 2017 (diff | hist) . . (+399) . . N Log e(z)=log(z) (Created page with "==Theorem== The following formula holds: $$\log_e(z)=\log(z),$$ where $\log_e$ denotes logarithm base a, $e$ denotes e, and $\log$ denotes logarithm. ==Proof== =...") (current)
- 19:25, 25 June 2017 (diff | hist) . . (+372) . . N Log a(b)=1/log b(a) (Created page with "==Theorem== The following formula holds: $$\log_a(z) = \dfrac{1}{\log_b(a)},$$ where $\log_a$ denotes logarithm base a. ==Proof== ==References== * {{BookReference|Handbo...")
- 19:23, 25 June 2017 (diff | hist) . . (+359) . . N Log base a in terms of logarithm base b (Created page with "==Theorem== The following formula holds: $$\log_a(z)=\dfrac{\log_b(z)}{\log_b(a)},$$ where $\log_a$ denotes logarithm base a. ==Proof== ==References== * {{BookReference|...") (current)
- 19:22, 25 June 2017 (diff | hist) . . (+376) . . N Logarithm base a (Created page with "The logarithm with base $a$, $\log_a$, is defined by $$\log_a(z)=\dfrac{\log(z)}{\log(a)},$$ where $\log$ denotes the logarithm. =Properties= =References= * {{BookRefere...")
- 19:20, 25 June 2017 (diff | hist) . . (-49) . . E is limit of (1+1/n)^n (current)
- 19:19, 25 June 2017 (diff | hist) . . (+27) . . Main Page (→Logarithm function and friends)
- 19:06, 25 June 2017 (diff | hist) . . (-107) . . Main Page (→External Links)
- 19:05, 25 June 2017 (diff | hist) . . (-93) . . Main Page (→External Links)
- 18:04, 25 June 2017 (diff | hist) . . (+48) . . Book:Johan Thim/Continuous Nowhere Differentiable Functions (current)
- 18:03, 25 June 2017 (diff | hist) . . (+65) . . Schwarz function (current)
- 18:02, 25 June 2017 (diff | hist) . . (+10) . . Darboux function (current)
- 18:01, 25 June 2017 (diff | hist) . . (+55) . . Darboux function
- 17:54, 25 June 2017 (diff | hist) . . (+18) . . Weierstrass nowhere differentiable function (→Videos) (current)
- 17:52, 25 June 2017 (diff | hist) . . (+182) . . N Weierstrass function is nowhere differentiable (Created page with "==Theorem== The Weierstrass function is nowhere differentiable. ==Proof== ==References== Category:Theorem Category:Unp...") (current)
- 17:51, 25 June 2017 (diff | hist) . . (+170) . . N Weierstrass function is continuous (Created page with "==Theorem== The Weierstrass function is continuous. ==Proof== ==References== Category:Theorem Category:Unproven") (current)
- 17:51, 25 June 2017 (diff | hist) . . (-158) . . Weierstrass nowhere differentiable function (→Properties)
- 17:48, 25 June 2017 (diff | hist) . . (0) . . Derivative of Legendre chi 2
- 17:48, 25 June 2017 (diff | hist) . . (+2) . . Legendre chi (current)
- 17:48, 25 June 2017 (diff | hist) . . (+42) . . N Derivative of Legendre chi (Tom moved page Derivative of Legendre chi to Derivative of Legendre chi 2) (current)
- 17:48, 25 June 2017 (diff | hist) . . (0) . . m Derivative of Legendre chi 2 (Tom moved page Derivative of Legendre chi to Derivative of Legendre chi 2)
- 03:40, 25 June 2017 (diff | hist) . . (+28) . . Main Page (→Special constants)
- 03:40, 25 June 2017 (diff | hist) . . (+26) . . Reciprocal Fibonacci constant (current)
- 03:26, 25 June 2017 (diff | hist) . . (-2) . . Square numbers (current)
- 03:26, 25 June 2017 (diff | hist) . . (+110) . . N Square numbers (Created page with "The square numbers are of the form $n^2$ where $n=0,1,2,\ldots$. =Properties= Definition:SpecialFunction")
- 03:07, 25 June 2017 (diff | hist) . . (+49) . . Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry (current)
- 03:06, 25 June 2017 (diff | hist) . . (+136) . . Hypergeometric pFq
- 03:03, 25 June 2017 (diff | hist) . . (+29) . . Lerch transcendent
- 03:03, 25 June 2017 (diff | hist) . . (+29) . . Dilogarithm (→Properties)
- 02:55, 25 June 2017 (diff | hist) . . (+138) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 02:54, 25 June 2017 (diff | hist) . . (+6) . . Li2(z)=zPhi(z,2,1)
- 02:53, 25 June 2017 (diff | hist) . . (0) . . Relationship between dilogarithm and log(1-z)/z
- 02:53, 25 June 2017 (diff | hist) . . (+32) . . N L 2(z)=zPhi(z,2,1) (Tom moved page L 2(z)=zPhi(z,2,1) to Li2(z)=zPhi(z,2,1)) (current)
- 02:53, 25 June 2017 (diff | hist) . . (0) . . m Li2(z)=zPhi(z,2,1) (Tom moved page L 2(z)=zPhi(z,2,1) to Li2(z)=zPhi(z,2,1))
- 02:52, 25 June 2017 (diff | hist) . . (+400) . . N Li2(z)=zPhi(z,2,1) (Created page with "==Theorem== The following formula holds: $$\mathrm{Li}_2(z)=z\Phi(z,2,1),$$ where $\mathrm{Li}_2$ denotes the dilogarithm and $\Phi$ denotes the Lerch transcendent. =...")
- 02:51, 25 June 2017 (diff | hist) . . (+139) . . Relationship between dilogarithm and log(1-z)/z
- 02:50, 25 June 2017 (diff | hist) . . (+163) . . Dilogarithm
- 02:47, 25 June 2017 (diff | hist) . . (+31) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 02:46, 25 June 2017 (diff | hist) . . (+198) . . Lerch transcendent
- 02:41, 25 June 2017 (diff | hist) . . (0) . . Clausen cosine
- 02:41, 25 June 2017 (diff | hist) . . (0) . . Clausen sine
- 00:50, 25 June 2017 (diff | hist) . . (-3) . . Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry (→Contents)
- 00:50, 25 June 2017 (diff | hist) . . (+60) . . Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry (→Contents)
- 00:43, 25 June 2017 (diff | hist) . . (+142) . . Error function (current)
- 00:42, 25 June 2017 (diff | hist) . . (+17) . . Sine integral (→References) (current)
- 00:42, 25 June 2017 (diff | hist) . . (+135) . . Sine integral
- 00:41, 25 June 2017 (diff | hist) . . (+75) . . Cosine integral
- 00:38, 25 June 2017 (diff | hist) . . (+73) . . Exponential integral Ei
- 00:35, 25 June 2017 (diff | hist) . . (+98) . . Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry
- 00:34, 25 June 2017 (diff | hist) . . (0) . . Gamma (→References)
- 00:33, 25 June 2017 (diff | hist) . . (+132) . . Gamma
- 00:33, 25 June 2017 (diff | hist) . . (-3) . . Beta (→References)
- 00:33, 25 June 2017 (diff | hist) . . (+136) . . Beta
- 00:10, 25 June 2017 (diff | hist) . . (+4) . . Reciprocal gamma written as an infinite product
- 00:06, 25 June 2017 (diff | hist) . . (+30) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 00:06, 25 June 2017 (diff | hist) . . (+194) . . Bernoulli numbers
- 00:02, 25 June 2017 (diff | hist) . . (+47) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 00:01, 25 June 2017 (diff | hist) . . (+987) . . Beta
- 23:58, 24 June 2017 (diff | hist) . . (+1,117) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I (→Contents)
- 23:56, 24 June 2017 (diff | hist) . . (-12) . . Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y)
- 23:54, 24 June 2017 (diff | hist) . . (+181) . . Beta in terms of sine and cosine
- 23:53, 24 June 2017 (diff | hist) . . (+484) . . N Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$ and $\mathrm{Re}(y)>0$: $$\displaystyle\int_{-1}^1 (1+t)^{2x-1}(1-t)^{2y-1}(1+t^2)^{-x-y} \mathrm{d}t= 2^{x+y-2}...")
- 23:51, 24 June 2017 (diff | hist) . . (+563) . . N Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (Created page with "==Theorem== The following formula holds for $z>0$, $\mathrm{Re}(y)>0$, and $\mathrm{Re}(x)>0$: $$\displaystyle\int_0^1 t^{x-1} (1-t^z)^{y-1} \mathrm{d}t = \dfrac{1}{z} B \left...")
- 23:45, 24 June 2017 (diff | hist) . . (+635) . . N Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (Created page with "==Theorem== The following formula holds for $z>0$, $b>0$, and $0 < \mathrm{Re} \left( \dfrac{x+1}{z} \right) < \mathrm{Re}(y)$: $$\displaystyle\int_0^{\infty} (1+bt^z)^{-y} t^...")
- 23:22, 24 June 2017 (diff | hist) . . (0) . . Integral of (t-b)^(x-1)(a-t)^(y-1)/(c-t)^(x+y) dt = (a-b)^(x+y-1)/((c-a)^x (c-b)^y) B(x,y)
- 23:21, 24 June 2017 (diff | hist) . . (+606) . . N Integral of (t-b)^(x-1)(a-t)^(y-1)/(c-t)^(x+y) dt = (a-b)^(x+y-1)/((c-a)^x (c-b)^y) B(x,y) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$, $\mathrm{Re}(y)>0$, and $b<a<c$: $$\displaystyle\int_a^b \dfrac{(t-b)^{x-1}(a-t)^{y-1}}{(c-t)^{x+y}} \mathrm{d}...")
- 23:18, 24 June 2017 (diff | hist) . . (+84) . . Integral of (t-b)^(x-1)(a-t)^(y-1)/(t-x)^(x+y) dt=(a-b)^(x+y-1)/((a-c)^x(b-c)^y) B(x,y)
- 23:17, 24 June 2017 (diff | hist) . . (+505) . . N Integral of (t-b)^(x-1)(a-t)^(y-1)/(t-x)^(x+y) dt=(a-b)^(x+y-1)/((a-c)^x(b-c)^y) B(x,y) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$, $\mathrm{Re}(y) > 0$, and $c<b<a$: $$\displaystyle\int_a^b \dfrac{(t-b)^{x-1}(a-t)^{y-1}}{(t-c)^{x+y}} \mathrm{...")
- 23:15, 24 June 2017 (diff | hist) . . (+530) . . N Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$, $\mathrm{Re}(y)>0$, and $b<a$: $$\displaystyle\int_a^b (t-b)^{x-1}(a-t)^{y-1} \mathrm{d}t=(a-b)^{x+y-1}B(x,y),$...")
- 23:13, 24 June 2017 (diff | hist) . . (+521) . . N Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (Created page with "==Theorem== The following formula holds for $b>0$, $\mathrm{Re}(x)>0$, and $\mathrm{Re}(y)>0$: $$\displaystyle\int_0^{\infty} t^{-x-1} (1+bt)^{-x-y} \mathrm{d}t=b^{-x}B(x,y),$...")
- 23:11, 24 June 2017 (diff | hist) . . (+518) . . N Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (Created page with "==Theorem== The following holds for $b>-1$, $\mathrm{Re}(x)>0$, and $\mathrm{Re}(y)>0$: $$\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1}(1+bt)^{-x-y} \mathrm{d}t = (1+b)^{-x} B(x,y)...")
- 23:09, 24 June 2017 (diff | hist) . . (+504) . . N B(x,y)=2^(1-x-y)integral (1+t)^(x-1)(1-t)^(y-1)+(1+t)^(y-1)(1-t)^(x-1) dt (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$ and $\mathrm{Re}(y)>0$: $$B(x,y) = 2^{1-x-y} \displaystyle\int_0^1 (1+t)^{x-1}(1-t)^{y-1} + (1+t)^{y-1}(1-t)^{x-...")
- 23:06, 24 June 2017 (diff | hist) . . (+67) . . 1/B(n,m)=n((n+m-1) choose (m-1))
- 23:05, 24 June 2017 (diff | hist) . . (+412) . . N 1/B(n,m)=n((n+m-1) choose (m-1)) (Created page with "==Theorem== The following formula holds: $$\dfrac{1}{B(n,m)} = n {{n+m-1} \choose {m-1}},$$ where $B$ denotes the beta function and ${{n+m-1} \choose {m-1}}$ denotes a b...")
- 23:04, 24 June 2017 (diff | hist) . . (+478) . . N 1/B(n,m)=m((n+m-1) choose (n-1)) (Created page with "==Theorem== The following formula holds: $$\dfrac{1}{B(n,m)} = m {{n+m-1} \choose {n-1}},$$ where $B$ denotes the beta function and ${{n+m-1} \choose {n-1}}$ denotes a b...")
- 23:02, 24 June 2017 (diff | hist) . . (+455) . . N B(x,y)B(x+y,z)B(x+y+z,u)=Gamma(x)Gamma(y)Gamma(z)Gamma(u)/Gamma(x+y+z+u) (Created page with "==Theorem== The following formula holds: $$B(x,y)B(x+y,z)B(x+y+z,u)=\dfrac{\Gamma(x)\Gamma(y)\Gamma(z)\Gamma(u)}{\Gamma(x+y+z+u)},$$ where $B$ denotes the beta function an...")
- 23:01, 24 June 2017 (diff | hist) . . (+394) . . N B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (Created page with "==Theorem== The following formula holds: $$B(x,y)B(x+y,z)=B(z,x)B(x+z,y),$$ where $B$ denotes the beta function. ==Proof== ==References== * {{BookReference|Higher Transc...")
- 22:59, 24 June 2017 (diff | hist) . . (+346) . . N B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (Created page with "==Theorem== The following formula holds: $$B(x,y)B(x+y,z)=B(y,z)B(y+z,x),$$ where $B$ denotes the beta function. ==Proof== ==References== * {{BookReference|Higher Transc...")
- 22:58, 24 June 2017 (diff | hist) . . (+345) . . N B(x,y+1)=(y/(x+y))B(x,y) (Created page with "==Theorem== The following formula holds: $$B(x,y+1)=\dfrac{y}{x+y} B(x,y),$$ where $B$ denotes the beta function. ==Proof== ==References== * {{BookReference|Higher Trans...")
- 22:57, 24 June 2017 (diff | hist) . . (+352) . . N B(x,y+1)=(y/x)B(x+1,y) (Created page with "==Theorem== The following formula holds: $$B(x,y+1)=\dfrac{y}{x} B(x+1,y),$$ where $B$ denotes the beta function. ==Proof== ==References== * {{BookReference|Higher Trans...")
- 22:56, 24 June 2017 (diff | hist) . . (+16) . . Beta as product of gamma functions
- 22:53, 24 June 2017 (diff | hist) . . (+33) . . Beta
- 22:52, 24 June 2017 (diff | hist) . . (+42) . . Beta as improper integral
- 22:51, 24 June 2017 (diff | hist) . . (+148) . . B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt
- 22:51, 24 June 2017 (diff | hist) . . (+42) . . Beta is symmetric
- 22:50, 24 June 2017 (diff | hist) . . (+230) . . N B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt (Created page with "==Theorem== The following formula holds: $$B(x,y) = \displaystyle\int_0^1 (t^{x-1}+t^{y-1})(1+t)^{-x-y} \mathrm{d}t,$$ where $B$ denotes the beta function. ==Proof== ==R...")
- 22:49, 24 June 2017 (diff | hist) . . (+59) . . Beta
- 19:38, 21 June 2017 (diff | hist) . . (+2) . . Book:Andrew Gray/A Treatise on Bessel Functions (→Contents) (current)
- 19:38, 21 June 2017 (diff | hist) . . (+17) . . Book:Andrew Gray/A Treatise on Bessel Functions (→Contents)
- 19:37, 21 June 2017 (diff | hist) . . (0) . . Bessel J (→References)
- 19:37, 21 June 2017 (diff | hist) . . (+125) . . Bessel J
- 19:31, 21 June 2017 (diff | hist) . . (+10) . . Book:Andrew Gray/A Treatise on Bessel Functions
- 19:31, 21 June 2017 (diff | hist) . . (-1) . . Reciprocal Riemann zeta in terms of Mobius (current)
- 19:30, 21 June 2017 (diff | hist) . . (+24) . . Reciprocal Riemann zeta in terms of Mobius
- 19:21, 21 June 2017 (diff | hist) . . (+22) . . Main Page (→Special functions)
- 19:20, 21 June 2017 (diff | hist) . . (+175) . . Pochhammer
- 19:20, 21 June 2017 (diff | hist) . . (+119) . . Hypergeometric pFq
- 19:19, 21 June 2017 (diff | hist) . . (+12) . . Hypergeometric 2F1
- 19:18, 21 June 2017 (diff | hist) . . (+118) . . Hypergeometric 2F1
- 22:39, 18 June 2017 (diff | hist) . . (+39) . . Main Page (→Hypergeometric series)
- 22:37, 18 June 2017 (diff | hist) . . (-271) . . Hypergeometric pFq
- 22:37, 18 June 2017 (diff | hist) . . (+32) . . Hypergeometric functions footer (current)
- 21:59, 17 June 2017 (diff | hist) . . (+345) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I (→Contents)
- 21:55, 17 June 2017 (diff | hist) . . (+1) . . 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z)
- 21:55, 17 June 2017 (diff | hist) . . (0) . . (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k)
- 21:53, 17 June 2017 (diff | hist) . . (+456) . . N Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (Created page with "==Theorem== The following formula holds: $$\dfrac{z}{1-\sqrt{q}} {}_2\phi_1 \left(q,\sqrt{q};\sqrt{q^3};z \right) = \displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{1-q^{k-\frac{1...")
- 21:52, 17 June 2017 (diff | hist) . . (+457) . . N 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) (Created page with "==Theorem== The following formula holds: $${}_2\phi_1(q,-1;-q;z)=1+2\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{1+q^k},$$ where ${}_2\phi_1$ denotes basic hypergeometric ph...")
- 21:50, 17 June 2017 (diff | hist) . . (+29) . . (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k)
- 21:49, 17 June 2017 (diff | hist) . . (+457) . . N (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k) (Created page with "==Theorem== The following formula holds: $$\dfrac{z}{1-z} {}_2\phi_1(q,q;q^2;z) = \displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{1-q^k},$$ where ${}_2\phi_1$ denotes basic hyp...")
- 21:47, 17 June 2017 (diff | hist) . . (+400) . . N 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) (Created page with "==Theorem== The following formula holds: $${}_1\phi_0(a;;z){}_1\phi_0(b;;z)={}_1\phi_0(ab;;z),$$ where ${}_1\phi_0$ denotes basic hypergeometric phi. ==Proof== ==Referen...")
- 21:44, 17 June 2017 (diff | hist) . . (+30) . . 1Phi0(a;;z) as infinite product
- 21:43, 17 June 2017 (diff | hist) . . (+48) . . Basic hypergeometric phi
- 21:42, 17 June 2017 (diff | hist) . . (-4) . . Hypergeometric pFq
- 21:42, 17 June 2017 (diff | hist) . . (-1) . . Hypergeometric pFq
- 21:41, 17 June 2017 (diff | hist) . . (-431) . . Hypergeometric pFq
- 21:39, 17 June 2017 (diff | hist) . . (-7) . . 1Phi0(a;;z) as infinite product
- 21:39, 17 June 2017 (diff | hist) . . (-7) . . Q-shifted factorial
- 21:39, 17 June 2017 (diff | hist) . . (-7) . . Exponential e in terms of basic hypergeometric phi (current)
- 21:38, 17 June 2017 (diff | hist) . . (-131) . . Exponential e in terms of basic hypergeometric phi
- 21:38, 17 June 2017 (diff | hist) . . (-7) . . Basic hypergeometric series psi (current)
- 21:38, 17 June 2017 (diff | hist) . . (+6) . . Jackson q-Bessel (1) (current)
- 21:38, 17 June 2017 (diff | hist) . . (+6) . . Jackson q-Bessel (2) (current)
- 21:38, 17 June 2017 (diff | hist) . . (+14) . . Jackson q-Bessel (2)
- 21:37, 17 June 2017 (diff | hist) . . (+28) . . Jackson q-Bessel (1)
- 21:37, 17 June 2017 (diff | hist) . . (-14) . . Jackson q-Bessel (1)
- 21:37, 17 June 2017 (diff | hist) . . (-14) . . Main Page
- 21:36, 17 June 2017 (diff | hist) . . (0) . . m Basic hypergeometric phi (Tom moved page Basic hypergeometric series phi to Basic hypergeometric phi)
- 21:36, 17 June 2017 (diff | hist) . . (+388) . . N 1Phi0(a;;z) as infinite product (Created page with "==Theorem== The following formula holds: $${}_1\phi_0(a;;z)=\displaystyle\prod_{k=0}^{\infty} \dfrac{1-aq^kz}{1-q^kz},$$ where ${}_1\phi_0$ denotes [[basic hypergeometric phi]...")
- 21:35, 17 June 2017 (diff | hist) . . (-3,196) . . Basic hypergeometric phi
- 21:33, 17 June 2017 (diff | hist) . . (+25) . . Q-shifted factorial
- 21:32, 17 June 2017 (diff | hist) . . (-102) . . Q-shifted factorial (→References)
- 21:32, 17 June 2017 (diff | hist) . . (+279) . . Q-shifted factorial
- 21:27, 17 June 2017 (diff | hist) . . (-253) . . Basic hypergeometric phi
- 20:31, 17 June 2017 (diff | hist) . . (+81) . . Hypergeometric 2F3 (current)
- 20:31, 17 June 2017 (diff | hist) . . (+81) . . Hypergeometric 1F1 (current)
- 20:30, 17 June 2017 (diff | hist) . . (+63) . . Hypergeometric 1F1
- 20:30, 17 June 2017 (diff | hist) . . (+373) . . N Hypergeometric 2F3 (Created page with "The hypergeometric series ${}_2F_3$ is defined by the series $${}_2F_3(a_1,a_2;b_1,b_2,b_3;z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k}{(b_1)_k(b_2)_k(b_3)_k}...")
- 20:28, 17 June 2017 (diff | hist) . . (+29) . . Main Page (→Hypergeometric series)
- 20:27, 17 June 2017 (diff | hist) . . (+72) . . Hypergeometric 4F1 (current)
- 20:27, 17 June 2017 (diff | hist) . . (+72) . . Hypergeometric 2F0 (current)
- 20:27, 17 June 2017 (diff | hist) . . (+29) . . Main Page (→Hypergeometric series)
- 20:27, 17 June 2017 (diff | hist) . . (+38) . . Hypergeometric 4F1
- 20:26, 17 June 2017 (diff | hist) . . (+302) . . N Hypergeometric 4F1 (Created page with "The hypergeometric ${}_4F_1$ function is defined by the series $${}_4F_1(a_1,a_2,a_3,a_4;b_1;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k(a_3)_k(a_4)_k}{(b_1)_k}...")
- 20:24, 17 June 2017 (diff | hist) . . (+29) . . Main Page (→Hypergeometric series)
- 20:24, 17 June 2017 (diff | hist) . . (+38) . . Hypergeometric 0F3 (current)
- 20:24, 17 June 2017 (diff | hist) . . (+332) . . N Hypergeometric 0F3 (Created page with "The hypergeometric ${}_0F_3$ function is defined by the series $${}_0F_3(;b_1,b_2,b_3;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(b_1)_k(b_2)_k(b_3)_k} \dfrac{z^k}{k!},$$ w...")
- 20:22, 17 June 2017 (diff | hist) . . (+56) . . Hypergeometric 0F1 (→Properties) (current)
- 20:21, 17 June 2017 (diff | hist) . . (+68) . . Hypergeometric 2F1
- 20:21, 17 June 2017 (diff | hist) . . (+68) . . Hypergeometric 0F1
- 20:21, 17 June 2017 (diff | hist) . . (+1) . . Hypergeometric 3F2 (→Properties) (current)
- 20:21, 17 June 2017 (diff | hist) . . (+7) . . Hypergeometric 2F1
- 20:20, 17 June 2017 (diff | hist) . . (+414) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I (→Contents)
- 20:18, 17 June 2017 (diff | hist) . . (+551) . . N 1F1(a;2a;z)1F1(b;2b;-z)=2F3(a/2+b/2,a/2+b/2+1/2;a+1/2,b+1/2,a+b;z^2/4) (Created page with "==Theorem== The following formula holds: $${}_1F_1(a;2a;z){}_1F_1(b;2b;-z)={}_2F_3 \left( \dfrac{a}{2} + \dfrac{b}{2}, \dfrac{a}{2} + \dfrac{b}{2} + \dfrac{1}{2}; a+\dfrac{1}{...")
- 20:12, 17 June 2017 (diff | hist) . . (+70) . . 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)
- 20:10, 17 June 2017 (diff | hist) . . (+492) . . N 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4) (Created page with "==Theorem== The following formula holds: $${}_1F_1(a;r;z){}_1F_1(a;r;-z)={}_2F_3\left(a, r-a; r, \dfrac{r}{2}, \dfrac{r}{2}+\dfrac{1}{2}; \dfrac{z^2}{4} \right),$$ where ${}_1...")
- 20:08, 17 June 2017 (diff | hist) . . (-166) . . 2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2)
- 20:08, 17 June 2017 (diff | hist) . . (+212) . . 2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2)
- 20:07, 17 June 2017 (diff | hist) . . (+506) . . N 2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2) (Created page with "==Theorem== The following formula holds: $${}_2F_0(a,b;;z){}_2F_0(a,b;;-z)={}_4F_1 \left(a, b, \dfrac{a}{2} + \dfrac{b}{2}, \dfrac{a}{2} + \dfrac{b}{2} + \dfrac{1}{2}; a+b; 4z...")
- 20:05, 17 June 2017 (diff | hist) . . (+55) . . 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4)
- 20:04, 17 June 2017 (diff | hist) . . (+489) . . N 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) (Created page with "==Theorem== The following formula holds: $${}_0F_1(;r;z){}_0F_1(;r;-z)={}_0F_3\left( ;r, \dfrac{r}{2}, \dfrac{r}{2} + \dfrac{1}{2}; - \dfrac{z^2}{4} \right),$$ where ${}_0F_1$...")
- 20:00, 17 June 2017 (diff | hist) . . (+39) . . 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z)
- 19:58, 17 June 2017 (diff | hist) . . (+501) . . N 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z) (Created page with "==Theorem== The following formula holds: $${}_0F_1(;r;z){}_0F_1(;s;z)={}_2F_1 \left( \dfrac{r}{2} + \dfrac{s}{2}, \dfrac{r}{2}+\dfrac{s}{2}-\dfrac{1}{2};r,s,r+s-1;4z \right),$...")
- 19:58, 17 June 2017 (diff | hist) . . (+57) . . 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)
- 19:33, 17 June 2017 (diff | hist) . . (+29) . . 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)
- 19:26, 17 June 2017 (diff | hist) . . (+59) . . 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)
- 19:25, 17 June 2017 (diff | hist) . . (+432) . . N 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z) (Created page with "==Theorem== The following formula holds: $${}_2F_1 \left( a,b;a+b +\dfrac{1}{2}; z \right)^2 = {}_3F_2 \left( 2a, a+b, 2b;a+b+\dfrac{1}{2}, 2a+2b;z \right),$$ where ${}_2F_1$...")
- 19:22, 17 June 2017 (diff | hist) . . (+29) . . Main Page (→Hypergeometric series)
- 19:21, 17 June 2017 (diff | hist) . . (+400) . . N Hypergeometric 3F2 (Created page with "The hypergeometric function ${}_3F_2$ is defined by $${}_3F_2(a_1,a_2,a_3; b_1,b_2; z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k(a_3)_k}{(b_1)_k(b_2)_k(b_3)_k}...")
- 19:17, 17 June 2017 (diff | hist) . . (+55) . . Hypergeometric 2F1
- 19:15, 17 June 2017 (diff | hist) . . (0) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 19:14, 17 June 2017 (diff | hist) . . (+89) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I (→Contents)
- 19:14, 17 June 2017 (diff | hist) . . (+120) . . Pochhammer symbol with non-negative integer subscript
- 19:11, 17 June 2017 (diff | hist) . . (+175) . . Pochhammer
- 19:11, 17 June 2017 (diff | hist) . . (+5) . . Hypergeometric pFq
- 19:10, 17 June 2017 (diff | hist) . . (+49) . . Pochhammer symbol with non-negative integer subscript
- 19:10, 17 June 2017 (diff | hist) . . (+232) . . N Pochhammer symbol with non-negative integer subscript (Created page with "==Theorem== The following formula holds: $$(a)_n = \left\{ \begin{array}{ll} 1, & \quad n=0 \\ a(a+1)\ldots(a+n-1), & \quad n=1,2,3,\ldots. \end{array} \right.$$ ==Proof== =...")
- 19:09, 17 June 2017 (diff | hist) . . (-52) . . Pochhammer (→Properties)
- 19:09, 17 June 2017 (diff | hist) . . (-19) . . Pochhammer (a+n)})
- 19:07, 17 June 2017 (diff | hist) . . (+26) . . Pochhammer
- 19:05, 17 June 2017 (diff | hist) . . (+52) . . Pochhammer
- 19:04, 17 June 2017 (diff | hist) . . (-23) . . Pochhammer
- 19:02, 17 June 2017 (diff | hist) . . (-146) . . Hypergeometric pFq (→External links)
- 19:08, 12 June 2017 (diff | hist) . . (-6) . . m Coshc (Reverted edits by 129.71.73.244 (talk) to last revision by Tom) (current)
- 02:54, 8 June 2017 (diff | hist) . . (+31) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 02:54, 8 June 2017 (diff | hist) . . (+210) . . Hypergeometric pFq
- 02:39, 8 June 2017 (diff | hist) . . (-106) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 02:36, 8 June 2017 (diff | hist) . . (+1,101) . . N Book:Ioannis Dimitrios Avgoustis/Definite Integration using the Generalized Hypergeometric Functions (Created page with "{{Book|Definite Integration using the Generalized Hypergeometric Functions|1977|Massachusetts Institute of Technology||Aleksandar Ivić}} ===Online copies=== [https://dspace....") (current)
- 23:53, 6 June 2017 (diff | hist) . . (+6) . . Limit of quotient of consecutive Fibonacci numbers (current)
- 23:16, 2 June 2017 (diff | hist) . . (+13) . . Gamma
- 02:02, 30 May 2017 (diff | hist) . . (+19) . . Book:Yudell L. Luke/The Special Functions And Their Approximations, Volume I (current)
- 01:54, 30 May 2017 (diff | hist) . . (+16) . . Gamma (→References)
- 01:54, 30 May 2017 (diff | hist) . . (+115) . . Gamma (→References)
- 01:52, 30 May 2017 (diff | hist) . . (+2,196) . . N Book:Yudell L. Luke/The Special Functions And Their Approximations, Volume I (Created page with "__NOTOC__ {{Book|Higher Transcendental Functions, Volume II|1969|Academic Press||Yudell L. Luke}} ===Online copies=== [https://archive.org/details/in.ernet.dli.2015.141299 h...")
- 01:33, 30 May 2017 (diff | hist) . . (+194) . . Paper:V.E. Hoggatt, Jr/Triangular numbers (→Contents) (current)
- 01:32, 30 May 2017 (diff | hist) . . (+34) . . Triangular numbers (→Properties) (current)
- 01:31, 30 May 2017 (diff | hist) . . (+372) . . N T(n+1)^2-T(n)^2=(n+1)^3 (Created page with "==Theorem== The following formula holds for $n=1,2,3,\ldots$: $$T(n+1)^2-T(n)^2=(n+1)^3,$$ where $T(n)$ denotes the $n$th triangular number. ==Proof==...") (current)
- 01:30, 30 May 2017 (diff | hist) . . (+17) . . T(n)^2=T(T(n))+T(T(n)-1) (current)
- 01:28, 30 May 2017 (diff | hist) . . (+8) . . Triangular numbers
- 01:28, 30 May 2017 (diff | hist) . . (+8) . . T(n)=n(n+1)/2 (current)
- 01:28, 30 May 2017 (diff | hist) . . (+8) . . T(n+1)=T(n)+n+1 (current)
- 01:27, 30 May 2017 (diff | hist) . . (+8) . . N^2=T(n)+T(n-1) (current)
- 01:27, 30 May 2017 (diff | hist) . . (+8) . . T(n)^2=T(T(n))+T(T(n)-1) (→References)
- 01:26, 30 May 2017 (diff | hist) . . (0) . . Triangular numbers
- 01:26, 30 May 2017 (diff | hist) . . (0) . . T(n)^2=T(T(n))+T(T(n)-1)
- 01:26, 30 May 2017 (diff | hist) . . (0) . . N^2=T(n)+T(n-1)
- 01:26, 30 May 2017 (diff | hist) . . (0) . . m T(n)^2=T(T(n))+T(T(n)-1) (Tom moved page T(n)^2=T(T(n))+T(T(n-1)) to T(n)^2=T(T(n))+T(T(n)-1))
- 01:25, 30 May 2017 (diff | hist) . . (+356) . . N T(n)^2=T(T(n))+T(T(n)-1) (Created page with "==Theorem== The following formula holds for $n=2,3,4,\ldots$: $$T(n)^2=T(T(n))+T(T(n-1)),$$ where $T(n)$ denotes the $n$th triangular number. ==Proof==...")
- 01:24, 30 May 2017 (diff | hist) . . (+18) . . N^2=T(n)+T(n-1)
- 01:24, 30 May 2017 (diff | hist) . . (+21) . . Triangular numbers
- 01:23, 30 May 2017 (diff | hist) . . (+21) . . T(n+1)=T(n)+n+1
- 01:23, 30 May 2017 (diff | hist) . . (+347) . . N N^2=T(n)+T(n-1) (Created page with "==Theorem== The following formula holds for $n=1,2,3,\ldots$: $$n^2=T(n)+T(n-1),$$ where $T(n)$ denotes the $n$th triangular number. ==Proof== ==Refer...")
- 01:22, 30 May 2017 (diff | hist) . . (+9) . . T(n+1)=T(n)+n+1
- 01:22, 30 May 2017 (diff | hist) . . (-1) . . Triangular numbers (→Properties)
- 01:22, 30 May 2017 (diff | hist) . . (-6) . . Triangular numbers
- 01:21, 30 May 2017 (diff | hist) . . (+31) . . T(n)=n(n+1)/2
- 01:21, 30 May 2017 (diff | hist) . . (+327) . . N T(n+1)=T(n)+n+1 (Created page with "==Theorem== The following formula holds: $$T(n+1) = T(n)+n+1,$$ where $T(n)$ denotes the $n$th triangular number. ==Proof== ==References== * {{PaperR...")
- 01:20, 30 May 2017 (diff | hist) . . (+295) . . N T(n)=n(n+1)/2 (Created page with "==Theorem== The following formula holds for all $n=1,2,3,\ldots$: $$T(n)=\dfrac{n(n+1)}{2},$$ where $T$ denotes triangular numbers. ==Proof== ==References== * {{PaperRef...")
- 01:18, 30 May 2017 (diff | hist) . . (-7) . . Triangular numbers
- 01:18, 30 May 2017 (diff | hist) . . (+20) . . Triangular numbers
- 01:18, 30 May 2017 (diff | hist) . . (-6) . . Triangular numbers (→References)
- 01:17, 30 May 2017 (diff | hist) . . (+188) . . Triangular numbers
- 01:14, 30 May 2017 (diff | hist) . . (+100) . . Triangular numbers
- 01:14, 30 May 2017 (diff | hist) . . (+26) . . Paper:V.E. Hoggatt, Jr/Triangular numbers
- 01:13, 30 May 2017 (diff | hist) . . (+240) . . N Paper:V.E. Hoggatt, Jr/Triangular numbers (Created page with "{{Book|Triangular numbers|1974|The Fibonacci Quarterly||V.E. Hoggatt, Jr}} ===Online copies=== [http://www.fq.math.ca/Issues/12-3.pdf hosted by the Fibonacci Quarterly]<br />...")
- 00:18, 30 May 2017 (diff | hist) . . (+54) . . Paper:Daniel S. Moak/The q-gamma function for q greater than 1 (→Contents) (current)
- 00:17, 30 May 2017 (diff | hist) . . (+120) . . Q-Gamma at z+1 (current)
- 00:16, 30 May 2017 (diff | hist) . . (+8) . . Q-shifted factorial (→References)
- 00:14, 30 May 2017 (diff | hist) . . (+108) . . Q-shifted factorial (→References)
- 00:13, 30 May 2017 (diff | hist) . . (+13) . . Q-Gamma (→References) (current)
- 00:13, 30 May 2017 (diff | hist) . . (+14) . . Q-shifted factorial
- 00:12, 30 May 2017 (diff | hist) . . (+18) . . Paper:Richard Askey/The q-Gamma and q-Beta functions (→Contents) (current)
- 00:11, 30 May 2017 (diff | hist) . . (0) . . Paper:Daniel S. Moak/The q-gamma function for q greater than 1
- 00:07, 30 May 2017 (diff | hist) . . (+8) . . Q-Gamma
- 00:01, 30 May 2017 (diff | hist) . . (+95) . . Q-Gamma (→References)
- 00:00, 30 May 2017 (diff | hist) . . (+6) . . Paper:Daniel S. Moak/The q-gamma function for q greater than 1 (→Contents)
- 00:00, 30 May 2017 (diff | hist) . . (+11) . . Paper:Daniel S. Moak/The q-gamma function for q greater than 1 (→Contents)
- 23:58, 29 May 2017 (diff | hist) . . (+280) . . N Paper:Daniel S. Moak/The q-gamma function for q greater than 1 (Created page with "{{Book|The q-gamma function for q greater than 1|1980|Aequationes Mathematicae||Daniel S. Moak|}} ===Online copies=== [http://gdz.sub.uni-goettingen.de/en/dms/loader/img/?PID...")
- 22:33, 25 May 2017 (diff | hist) . . (+44) . . Paper:John H. Halton/On a General Fibonacci Identity (current)
- 22:33, 25 May 2017 (diff | hist) . . (+106) . . F(-n)=(-1)^(n+1)F(n) (current)
- 22:32, 25 May 2017 (diff | hist) . . (+122) . . Binet's formula (current)
- 22:31, 25 May 2017 (diff | hist) . . (+9) . . Fibonacci numbers (→References)
- 22:05, 25 May 2017 (diff | hist) . . (+85) . . Fibonacci numbers
- 22:04, 25 May 2017 (diff | hist) . . (0) . . m Paper:John H. Halton/On a General Fibonacci Identity (Tom moved page John H. Halton/On a General Fibonacci Identity to Paper:John H. Halton/On a General Fibonacci Identity)
- 22:03, 25 May 2017 (diff | hist) . . (+254) . . N Paper:John H. Halton/On a General Fibonacci Identity (Created page with "{{Book|On a General Fibonacci Identity|1965|The Fibonacci Quarterly||John H. Halton}} ===Online copies=== [http://www.fq.math.ca/Scanned/3-1/halton.pdf hosted by the Fibonacc...")
- 00:57, 25 May 2017 (diff | hist) . . (+10) . . Lucas numbers (current)
- 00:55, 25 May 2017 (diff | hist) . . (+226) . . Lucas numbers (→Properties)
- 00:53, 25 May 2017 (diff | hist) . . (+2) . . Reciprocal Fibonacci constant
- 00:53, 25 May 2017 (diff | hist) . . (+1) . . Limit of quotient of consecutive Fibonacci numbers
- 00:52, 25 May 2017 (diff | hist) . . (+1) . . Catalan's identity (current)
- 00:52, 25 May 2017 (diff | hist) . . (0) . . m Catalan's identity (Tom moved page Catalan's identity for the Fibonacci sequence to Catalan's identity)
- 00:52, 25 May 2017 (diff | hist) . . (+32) . . N Catalan's identity for the Fibonacci sequence (Tom moved page Catalan's identity for the Fibonacci sequence to Catalan's identity) (current)
- 00:51, 25 May 2017 (diff | hist) . . (+235) . . Fibonacci numbers (→Properties)
- 00:41, 25 May 2017 (diff | hist) . . (+423) . . Paper:S.L. Basin/A Primer on the Fibonacci Sequence Part I (→Contents) (current)
- 00:39, 25 May 2017 (diff | hist) . . (+342) . . N L(-n)=(-1)^nL(n) (Created page with "==Theorem== The following formula holds: $$L(-n)=(-1)^{n}L(n),$$ where $L(n)$ denotes the $n$th Lucas number. ==Proof== ==References== * {{PaperReference|A...") (current)
- 00:38, 25 May 2017 (diff | hist) . . (+363) . . N F(-n)=(-1)^(n+1)F(n) (Created page with "==Theorem== The following formula holds: $$F(-n)=(-1)^{n+1}F(n),$$ where $F(n)$ denotes the $n$th Fibonacci number. ==Proof== ==References== * {{PaperR...")
- 00:37, 25 May 2017 (diff | hist) . . (+437) . . N L(n)^2-5F(n)^2=4(-1)^n (Created page with "==Theorem== The following formula holds: $$L(n)^2-5F(n)^2=4(-1)^n,$$ where $L(n)$ denotes the $n$th Lucas number and $F(n)$ denotes the $n$th Fibonacci num...") (current)
- 00:35, 25 May 2017 (diff | hist) . . (+169) . . Sum of squares of Fibonacci numbers (current)
- 00:33, 25 May 2017 (diff | hist) . . (+402) . . N F(n+m+1)=F(n+1)F(m+1)+F(n)F(m) (Created page with "==Theorem== The following formula holds: $$F(n+m+1)=F(n+1)F(m+1)+F(n)F(m),$$ where $F(n)$ denotes a Fibonacci number. ==Proof== ==References== * {{Pape...") (current)
- 00:32, 25 May 2017 (diff | hist) . . (+417) . . N F(2n)=F(n)L(n) (Created page with "==Theorem== The following formula holds: $$F(2n)=F(n)L(n),$$ where $F(n)$ denotes a Fibonacci number and $L(n)$ denotes a Lucas number....") (current)
- 00:30, 25 May 2017 (diff | hist) . . (+358) . . N F(2n)=F(n+1)^2-F(n-1)^2 (Created page with "==Theorem== The following formula holds: $$F(2n)=F(n+1)^2-F(n-1)^2,$$ where $F(n)$ denotes a Fibonacci number. ==Proof== ==References== * {{PaperRefere...") (current)
- 00:29, 25 May 2017 (diff | hist) . . (+23) . . F(2n+1)=F(n+1)^2+F(n)^2 (current)
- 00:29, 25 May 2017 (diff | hist) . . (+339) . . N F(2n+1)=F(n+1)^2+F(n)^2 (Created page with "==Theorem== The following formula holds: $$F(2n+1)=F(n+1)^2+F(n)^2,$$ where $F(n)$ denotes a Fibonacci number. ==Proof== ==References== * {{PaperRefere...")
- 00:28, 25 May 2017 (diff | hist) . . (+17) . . L(n)=F(n+1)+F(n-1) (current)
- 00:26, 25 May 2017 (diff | hist) . . (+29) . . Lucas numbers
- 00:26, 25 May 2017 (diff | hist) . . (+405) . . N L(n)=F(n+1)+F(n-1) (Created page with "==Theorem== The following formula holds: $$L(n)=F(n+1)+F(n-1),$$ where $L(n)$ denotes a Lucas number and $F(n)$ denotes a Fibonacci numbers|Fibonacci numbe...")
- 00:25, 25 May 2017 (diff | hist) . . (+12) . . L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1) (current)
- 00:24, 25 May 2017 (diff | hist) . . (+29) . . Fibonacci numbers (→Properties)
- 00:23, 25 May 2017 (diff | hist) . . (+14) . . L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1)
- 00:22, 25 May 2017 (diff | hist) . . (+339) . . N L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1) (Created page with "==Theorem== The following formula holds: $$L(n+1)L(n-1)-L(n)^2=5(-1)^{n+1},$$ where $L(n)$ denotes a Lucas number. ==Proof== ==References== * {{PaperReference|A Primer o...")
- 00:21, 25 May 2017 (diff | hist) . . (+25) . . F(n+1)F(n-1)-F(n)^2=(-1)^n (current)
- 00:20, 25 May 2017 (diff | hist) . . (+332) . . N F(n+1)F(n-1)-F(n)^2=(-1)^n (Created page with "==Theorem== The following formula holds: $$F(n+1)F(n-1)-F(n)^2=(-1)^n,$$ where $F(n)$ denotes a Fibonacci number. ==Proof== ==References== * {{PaperReference|A Primer on...")
- 00:19, 25 May 2017 (diff | hist) . . (+20) . . Sum of Lucas numbers (current)
- 00:18, 25 May 2017 (diff | hist) . . (+37) . . Fibonacci numbers (→Properties)
- 00:17, 25 May 2017 (diff | hist) . . (+45) . . Lucas numbers
- 00:17, 25 May 2017 (diff | hist) . . (+369) . . N Sum of Lucas numbers (Created page with "==Theorem== The following formula holds: $$\displaystyle\sum_{k=1}^n L(k) = L(n+2)-3,$$ where $L(k)$ denotes the $k$th Lucas number. ==Proof== ==References...")
- 00:15, 25 May 2017 (diff | hist) . . (+151) . . Sum of Fibonacci numbers (current)
- 00:11, 25 May 2017 (diff | hist) . . (+89) . . Fibonacci numbers
- 00:10, 25 May 2017 (diff | hist) . . (+459) . . N Lucas numbers (Created page with "The Lucas numbers, $L \colon \mathbb{Z} \rightarrow \mathbb{Z}$, is the solution to the following initial value problem: $$L(n+2)=L(n)+L(n+1), \quad L(0)=2, L(1)=1.$$ =See al...")
- 00:02, 25 May 2017 (diff | hist) . . (+7) . . Fibonacci numbers (→References)
- 00:01, 25 May 2017 (diff | hist) . . (+118) . . Fibonacci numbers
- 00:00, 25 May 2017 (diff | hist) . . (+29) . . Paper:S.L. Basin/A Primer on the Fibonacci Sequence Part I
- 23:57, 24 May 2017 (diff | hist) . . (+265) . . N Paper:S.L. Basin/A Primer on the Fibonacci Sequence Part I (Created page with "{{Book|A Primer on the Fibonacci Sequence Part I|1963|The Fibonacci Quarterly||S.L. Basin|author2=V.E. Hoggatt, Jr.}} ===Online copies=== [http://www.fq.math.ca/Scanned/1-1/p...")
- 13:08, 24 May 2017 (diff | hist) . . (+23) . . Main Page (→Special sequences)
- 00:33, 24 May 2017 (diff | hist) . . (+8) . . Catalan's identity
- 00:31, 24 May 2017 (diff | hist) . . (-1) . . Main Page
- 00:30, 24 May 2017 (diff | hist) . . (-1) . . Catalan's identity
- 00:30, 24 May 2017 (diff | hist) . . (+7) . . Sum of squares of Fibonacci numbers
- 00:30, 24 May 2017 (diff | hist) . . (+8) . . Sum of even indexed Fibonacci numbers (current)
- 00:29, 24 May 2017 (diff | hist) . . (+10) . . Sum of odd indexed Fibonacci numbers (current)
- 00:28, 24 May 2017 (diff | hist) . . (+7) . . Sum of Fibonacci numbers
- 00:28, 24 May 2017 (diff | hist) . . (-1) . . Paper:Maruti Ram Murty/The Fibonacci Zeta Function (current)
- 00:28, 24 May 2017 (diff | hist) . . (-1) . . Binet's formula
- 00:27, 24 May 2017 (diff | hist) . . (+21) . . Limit of quotient of consecutive Fibonacci numbers
- 00:27, 24 May 2017 (diff | hist) . . (-1) . . Paper:Edmund Landau/Sur la série des inverse de nombres de Fibonacci (current)
- 00:26, 24 May 2017 (diff | hist) . . (+3) . . Reciprocal Fibonacci constant
- 00:25, 24 May 2017 (diff | hist) . . (-1) . . Fibonacci zeta function (current)
- 00:25, 24 May 2017 (diff | hist) . . (+3) . . Fibonacci zeta function
- 00:24, 24 May 2017 (diff | hist) . . (0) . . m Fibonacci numbers (Tom moved page Fibonacci sequence to Fibonacci numbers)
- 00:21, 24 May 2017 (diff | hist) . . (+2) . . Golden ratio (current)
- 00:21, 24 May 2017 (diff | hist) . . (+18) . . Fibonacci numbers
- 00:55, 23 May 2017 (diff | hist) . . (+106) . . Devil's staircase (→Videos)
- 18:40, 12 May 2017 (diff | hist) . . (-100) . . Riemann zeta (→Videos) (current)
- 18:39, 12 May 2017 (diff | hist) . . (+100) . . Riemann zeta (→Videos)
- 22:54, 11 May 2017 (diff | hist) . . (-1) . . Riemann zeta (→Videos)
- 22:53, 11 May 2017 (diff | hist) . . (+6) . . Riemann zeta (→Videos)
- 22:44, 11 May 2017 (diff | hist) . . (+95) . . Riemann zeta (→Videos)
- 23:05, 8 May 2017 (diff | hist) . . (+197) . . N Komornik–Loreti constant (Created page with "The Komornik-Loreti constant $q$ is defined so that $$\displaystyle\sum_{k=1}^{\infty} \dfrac{t_k}{q^k}=1,$$ where $t_k$ denotes a term in the Thue-Morse sequence. Cate...") (current)
- 22:45, 8 May 2017 (diff | hist) . . (+66) . . Main Page (→Special constants)
- 16:21, 29 April 2017 (diff | hist) . . (-26) . . Main Page (→Special functions)
- 16:21, 29 April 2017 (diff | hist) . . (+158) . . Bessel functions footer (current)
- 16:18, 29 April 2017 (diff | hist) . . (+998) . . N File:Besselcliffordglyph.png (Category:besselcliffordglyph <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 2.4,2.4 def besselclifford(n,z): return nsum(lambda k: z**k...) (current)
- 16:03, 29 April 2017 (diff | hist) . . (+1) . . Bessel-Clifford (current)
- 16:03, 29 April 2017 (diff | hist) . . (+120) . . Bessel-Clifford
- 16:03, 29 April 2017 (diff | hist) . . (+557) . . N File:Besselcliffordn=0plot.png (Category:Plot <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 10, 10 def besselclifford(n,z): return nsum(lambda k: z**k/(gamma(k+n+1)*...) (current)
- 15:57, 29 April 2017 (diff | hist) . . (-9) . . Main Page (→Special functions)
- 00:35, 26 April 2017 (diff | hist) . . (+16) . . Derivative of tangent (→Proof) (current)
- 00:34, 26 April 2017 (diff | hist) . . (+15) . . Derivative of secant (→Proof) (current)
- 23:49, 25 April 2017 (diff | hist) . . (+8) . . Erdős-Borwein Constant is irrational (current)
- 17:06, 19 April 2017 (diff | hist) . . (0) . . Polylogarithm
- 17:03, 19 April 2017 (diff | hist) . . (0) . . Polylogarithm
- 22:45, 28 March 2017 (diff | hist) . . (-34) . . Antiderivative of arcsin (current)
- 21:15, 28 March 2017 (diff | hist) . . (+583) . . Antiderivative of arccos (current)
- 21:11, 28 March 2017 (diff | hist) . . (+17) . . Integration by parts (current)
- 21:11, 28 March 2017 (diff | hist) . . (+4) . . Integration by parts
- 04:11, 28 March 2017 (diff | hist) . . (+72) . . Exsecant (current)
- 03:52, 28 March 2017 (diff | hist) . . (+242) . . N Hacoversine (Created page with "The hacoversine function $\mathrm{hacoversin} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\mathrm{hacoversin}(z) = \dfrac{1-\sin(z)}{2},$$ where $\sin$ denotes [...") (current)
- 03:51, 28 March 2017 (diff | hist) . . (-5) . . Vercosine (current)
- 03:51, 28 March 2017 (diff | hist) . . (-10) . . Havercosine (current)
- 03:50, 28 March 2017 (diff | hist) . . (+241) . . N Hacovercosine (Created page with "The hacovercosine function $\mathrm{hacovercos} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\mathrm{hacovercos}(z)=\dfrac{1+\sin(z)}{2},$$ where $\sin$ denotes [...") (current)
- 03:49, 28 March 2017 (diff | hist) . . (-1) . . Exsecant
- 03:48, 28 March 2017 (diff | hist) . . (+226) . . N Vercosine (Created page with "The vercosine function $\mathrm{vercos} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\mathrm{vercos}(z)=1+\cos(\theta),$$ where $\cos$ denotes cosine. =Prop...")
- 03:47, 28 March 2017 (diff | hist) . . (+20) . . Main Page (→Depreciated trigonometric functions)
- 03:47, 28 March 2017 (diff | hist) . . (+221) . . N Covercosine (Created page with "The coversine function $\mathrm{coversin} \colon \mathbb{C} \rightarrow \mathbb{C}$ defined by $$\mathrm{coversin}(z) = 1-\sin(z),$$ where $\sin$ denotes sine. =Propertie...") (current)
- 03:45, 28 March 2017 (diff | hist) . . (+33) . . Havercosine
- 03:45, 28 March 2017 (diff | hist) . . (-25) . . Haversine (current)
- 03:45, 28 March 2017 (diff | hist) . . (+216) . . N Havercosine (Created page with "The havercosine function $\mathrm{havercos} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\mathrm{havercos}(\theta) = \dfrac{1+\cos(\theta)}{2}.$$ =Properties= =...")
- 03:41, 28 March 2017 (diff | hist) . . (0) . . Error function is odd (→Proof) (current)
- 03:41, 28 March 2017 (diff | hist) . . (-43) . . Error function is odd
- 03:41, 28 March 2017 (diff | hist) . . (+432) . . Error function is odd (→Proof)
- 20:15, 25 March 2017 (diff | hist) . . (+14) . . Pell constant (current)
- 15:31, 18 March 2017 (diff | hist) . . (-13) . . Riemann xi (current)
- 15:31, 18 March 2017 (diff | hist) . . (+10) . . Riemann xi
- 15:29, 18 March 2017 (diff | hist) . . (+268) . . N Riemann-Landau xi is even (Created page with "==Theorem== Riemann-Landau xi is an even function. ==Proof== ==References== * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Rieman...") (current)
- 15:28, 18 March 2017 (diff | hist) . . (+403) . . N Riemann-Landau xi (Created page with "The Riemann-Landau $\Xi$ function is defined by $$\Xi(z) = \xi \left( \dfrac{1}{2} + iz \right),$$ where $\xi$ denotes Riemann xi. =Properties= Riemann-Landau xi is eve...") (current)
- 15:27, 18 March 2017 (diff | hist) . . (+17) . . Functional equation for Riemann xi (→References) (current)
- 15:25, 18 March 2017 (diff | hist) . . (+28) . . Main Page (→Special functions)
- 15:23, 18 March 2017 (diff | hist) . . (+72) . . Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann (current)
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