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- 21:03, 3 March 2018 (diff | hist) . . (+82) . . Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (current)
- 21:03, 3 March 2018 (diff | hist) . . (+82) . . Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (current)
- 21:02, 3 March 2018 (diff | hist) . . (+82) . . Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (current)
- 21:02, 3 March 2018 (diff | hist) . . (+82) . . 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 (current)
- 21:02, 3 March 2018 (diff | hist) . . (+82) . . 1/B(n,m)=n((n+m-1) choose (m-1)) (current)
- 21:01, 3 March 2018 (diff | hist) . . (+82) . . 1/B(n,m)=m((n+m-1) choose (n-1)) (current)
- 21:01, 3 March 2018 (diff | hist) . . (+82) . . 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) (current)
- 20:58, 3 March 2018 (diff | hist) . . (+82) . . B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (current)
- 20:58, 3 March 2018 (diff | hist) . . (+82) . . B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (current)
- 20:58, 3 March 2018 (diff | hist) . . (+82) . . B(x,y+1)=(y/(x+y))B(x,y) (current)
- 20:58, 3 March 2018 (diff | hist) . . (+82) . . B(x,y+1)=(y/x)B(x+1,y) (current)
- 20:58, 3 March 2018 (diff | hist) . . (+82) . . Beta as product of gamma functions (current)
- 20:57, 3 March 2018 (diff | hist) . . (+82) . . Beta is symmetric (current)
- 20:57, 3 March 2018 (diff | hist) . . (+82) . . B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt (current)
- 20:57, 3 March 2018 (diff | hist) . . (+82) . . Beta as improper integral (current)
- 20:57, 3 March 2018 (diff | hist) . . (+82) . . Beta
- 20:57, 3 March 2018 (diff | hist) . . (+82) . . Euler-Mascheroni constant (current)
- 20:56, 3 March 2018 (diff | hist) . . (+82) . . Reciprocal gamma written as an infinite product (current)
- 20:56, 3 March 2018 (diff | hist) . . (+82) . . Gamma function written as infinite product (current)
- 20:56, 3 March 2018 (diff | hist) . . (+82) . . Gamma function written as a limit of a factorial, exponential, and a rising factorial (current)
- 20:56, 3 March 2018 (diff | hist) . . (+82) . . Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0 (current)
- 20:56, 3 March 2018 (diff | hist) . . (+82) . . Gamma
- 20:55, 3 March 2018 (diff | hist) . . (+80) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 20:54, 3 March 2018 (diff | hist) . . (+2) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 20:53, 3 March 2018 (diff | hist) . . (0) . . m Book:Arthur Erdélyi/Higher Transcendental Functions Volume I (Tom moved page Book:Harry Bateman/Higher Transcendental Functions Volume I to Book:Arthur Erdélyi/Higher Transcendental Functions Volume I)
- 20:53, 3 March 2018 (diff | hist) . . (+75) . . N Book:Harry Bateman/Higher Transcendental Functions Volume I (Tom moved page Book:Harry Bateman/Higher Transcendental Functions Volume I to Book:Arthur Erdélyi/Higher Transcendental Functions Volume I) (current)
- 03:22, 26 February 2018 (diff | hist) . . (+46) . . Book:Nicholas Higham/Functions of Matrices: Theory and Computation (current)
- 03:20, 26 February 2018 (diff | hist) . . (+6) . . Modular form (current)
- 03:20, 26 February 2018 (diff | hist) . . (+21) . . Modular form
- 03:19, 26 February 2018 (diff | hist) . . (+501) . . N Modular form (Created page with "A modular form of weight $k$ for $\mathrm{SL}(2,\mathbb{Z})$ is a function $f \colon \mathbb{H} \rightarrow \mathbb{C}$, where $\mathbb{H}$ is a the upper half-plane that sati...")
- 03:10, 26 February 2018 (diff | hist) . . (+23) . . Matrix exponential (current)
- 03:10, 26 February 2018 (diff | hist) . . (+377) . . N Matrix e^A=limit of (I+A/s)^s (Created page with "==Theorem== The following formula holds for any matrix $A \in \mathbb{C}^{n \times n}$: $$e^A = \displaystyle\lim_{s \rightarrow \infty} \left( I + \dfrac{A}{s} \right)^s.$$...") (current)
- 15:46, 25 February 2018 (diff | hist) . . (+474) . . Catalan's constant using Legendre chi (current)
- 15:40, 25 February 2018 (diff | hist) . . (0) . . Catalan's constant (current)
- 04:28, 24 February 2018 (diff | hist) . . (0) . . Book:Nicholas Higham/Functions of Matrices: Theory and Computation
- 04:28, 24 February 2018 (diff | hist) . . (+35) . . Book:Nicholas Higham/Functions of Matrices: Theory and Computation
- 04:27, 24 February 2018 (diff | hist) . . (+40) . . Matrix exponential
- 04:26, 24 February 2018 (diff | hist) . . (+121) . . Matrix exponential
- 04:16, 24 February 2018 (diff | hist) . . (+2,234) . . Book:Nicholas Higham/Functions of Matrices: Theory and Computation
- 04:06, 24 February 2018 (diff | hist) . . (+5,025) . . N Book:Nicholas Higham/Functions of Matrices: Theory and Computation (Created page with "{{Book|Functions of Matrices: Theory and Computation|2008|||Nicholas Higham}} :List of Figures :List of Tables :Preface :1 Theory of Matrix Functions ::1.1 Introduction ::1.2...")
- 02:28, 24 February 2018 (diff | hist) . . (+23) . . Main Page (→*-integral functions)
- 02:25, 24 February 2018 (diff | hist) . . (+175) . . N Entire exponential integral (Created page with "The $\mathrm{Ein}$ function is defined by $$\mathrm{Ein}(z)=\displaystyle\int_0^z \dfrac{1-e^{-t}}{t} \mathrm{d}t.$$ =Properties= =References= Category:SpecialFunction")
- 02:01, 24 February 2018 (diff | hist) . . (+2) . . Integral of (z^n)log(z)dz=(z^(n+1)/(n+1))log(z)-z^(n+1)/(n+1)^2 for integer n neq -1 (current)
- 01:48, 24 February 2018 (diff | hist) . . (0) . . Coth of a sum (current)
- 23:18, 20 February 2018 (diff | hist) . . (+88) . . Integral of Bessel J for nu=1 (current)
- 23:17, 20 February 2018 (diff | hist) . . (+21) . . Integral of Bessel J for nu=1
- 23:16, 20 February 2018 (diff | hist) . . (+109) . . Integral of Bessel J for nu=1
- 23:15, 20 February 2018 (diff | hist) . . (+112) . . Integral of Bessel J for nu=1
- 23:14, 20 February 2018 (diff | hist) . . (+506) . . Integral of Bessel J for nu=1
- 23:10, 20 February 2018 (diff | hist) . . (+124) . . Integral of Bessel J for nu=1
- 05:20, 12 February 2018 (diff | hist) . . (-6) . . Dedekind eta (current)
- 05:20, 12 February 2018 (diff | hist) . . (+35) . . Dedekind eta
- 05:17, 12 February 2018 (diff | hist) . . (+73) . . Dedekind eta (→Properties)
- 04:52, 12 February 2018 (diff | hist) . . (+33) . . Paper:Yilmaz Simsek/q-Dedekind type sums related to q-zeta function and basic L-series (current)
- 04:51, 12 February 2018 (diff | hist) . . (+9) . . Q-zeta (→References) (current)
- 04:51, 12 February 2018 (diff | hist) . . (+487) . . N Q-Hurwitz zeta (Created page with "Let $|q|<1$. The $q$-Hurwitz zeta function $\zeta_q \colon \mathbb{C} \times (0,1] \rightarrow \mathbb{C}$ is defined by $$\zeta_q(z,x)=\displaystyle\sum_{k=0}^{\infty} \dfra...") (current)
- 17:49, 11 February 2018 (diff | hist) . . (+68) . . Main Page (→Zeta functions)
- 17:48, 11 February 2018 (diff | hist) . . (+42) . . Main Page (→$q$-special functions)
- 17:48, 11 February 2018 (diff | hist) . . (+53) . . Q-zeta
- 17:47, 11 February 2018 (diff | hist) . . (-4) . . Q-zeta
- 17:46, 11 February 2018 (diff | hist) . . (+36) . . Q-zeta
- 17:44, 11 February 2018 (diff | hist) . . (+11) . . Q-zeta
- 17:44, 11 February 2018 (diff | hist) . . (+132) . . Q-zeta
- 17:43, 11 February 2018 (diff | hist) . . (+1) . . Paper:Yilmaz Simsek/q-Dedekind type sums related to q-zeta function and basic L-series
- 17:42, 11 February 2018 (diff | hist) . . (+326) . . N Paper:Yilmaz Simsek/q-Dedekind type sums related to q-zeta function and basic L-series (Created page with "{{Book|q-Dedekind type sums related to q-zeta function and basic L-series|2006|Journal of Mathematical Analysis and Applications||Yilmaz Simsek}} ===Online copies=== [https:/...")
- 17:37, 11 February 2018 (diff | hist) . . (+277) . . N Q-zeta (Created page with "The $q$-zeta function $\zeta_q \colon \mathbb{C} \times (0,1] \rightarrow \mathbb{C}$ by $$\zeta_q(z,x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{q^{-k}}{(q^{-k}[k]+x)^z},$$ whe...")
- 17:32, 11 February 2018 (diff | hist) . . (+9) . . Main Page (→$q$-special functions)
- 17:32, 11 February 2018 (diff | hist) . . (+17) . . Main Page (→$q$-calculus)
- 05:12, 11 February 2018 (diff | hist) . . (+46) . . Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition
- 05:12, 11 February 2018 (diff | hist) . . (+256) . . Signum (current)
- 05:10, 11 February 2018 (diff | hist) . . (+120) . . Signum
- 18:50, 9 January 2018 (diff | hist) . . (-11) . . Main Page
- 18:50, 9 January 2018 (diff | hist) . . (+230) . . Main Page
- 21:55, 2 January 2018 (diff | hist) . . (+11) . . E(2,1)(-z^2)=cos(z) (current)
- 21:35, 2 January 2018 (diff | hist) . . (+142) . . Mittag-Leffler (current)
- 21:35, 2 January 2018 (diff | hist) . . (+182) . . Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications (current)
- 21:34, 2 January 2018 (diff | hist) . . (+13) . . E(1,1)(z)=exp(z) (current)
- 21:33, 2 January 2018 (diff | hist) . . (-25) . . E(2,1)(z)=cosh(sqrt(z)) (current)
- 21:32, 2 January 2018 (diff | hist) . . (+468) . . N E(2,1)(-z^2)=cos(z) (Created page with "==Theorem== The following formula holds for $z \in \mathbb{C}$: $$E_{2,1}(-z^2)=\cos(z),$$ where $E_{2,1}$ denotes the Mittag-Leffler function and $\cos$ denotes [[cosine]...")
- 21:31, 2 January 2018 (diff | hist) . . (+19) . . E(2,1)(z)=cosh(sqrt(z))
- 21:29, 2 January 2018 (diff | hist) . . (0) . . E(1,1)(z)=exp(z)
- 21:28, 2 January 2018 (diff | hist) . . (+484) . . N E(2,1)(z)=cosh(sqrt(z)) (Created page with "==Theorem== The following formula holds: $$E_{2,1}(z)=\cosh(\sqrt{z}),$$ where $E_{2,1}$ denotes the Mittag-Leffler function and $\cosh$ denotes cosh. ==Proof== ==Re...")
- 21:28, 2 January 2018 (diff | hist) . . (+13) . . Mittag-Leffler
- 21:27, 2 January 2018 (diff | hist) . . (+55) . . N E (0,1)(z)=1/(1-z) for (Tom moved page E (0,1)(z)=1/(1-z) for to E (0,1)(z)=1/(1-z) for abs(z) less than 1) (current)
- 21:27, 2 January 2018 (diff | hist) . . (0) . . m E (0,1)(z)=1/(1-z) for abs(z) less than 1 (Tom moved page E (0,1)(z)=1/(1-z) for to E (0,1)(z)=1/(1-z) for abs(z) less than 1) (current)
- 21:24, 2 January 2018 (diff | hist) . . (+468) . . N E(1,1)(z)=exp(z) (Created page with "==Theorem== The following formula holds: $$E_{1,1}(z)=e^z,$$ where $E_{1,1}$ denotes the Mittag-Leffler function and $e^z$ denotes the exponential. ==Proof== ==Refer...")
- 21:22, 2 January 2018 (diff | hist) . . (+432) . . N E (0,1)(z)=1/(1-z) for abs(z) less than 1 (Created page with "==Theorem== The following formula holds for $|z|<1$: $$E_{0,1}(z)=\dfrac{1}{1-z},$$ where $E_{0,1}$ denotes the Mittag-Leffler function. ==Proof== ==References== * {{Pap...")
- 21:21, 2 January 2018 (diff | hist) . . (+23) . . Mittag-Leffler
- 21:17, 2 January 2018 (diff | hist) . . (+35) . . Mittag-Leffler
- 21:13, 2 January 2018 (diff | hist) . . (+35) . . Mittag-Leffler
- 21:09, 2 January 2018 (diff | hist) . . (+141) . . Mittag-Leffler
- 21:08, 2 January 2018 (diff | hist) . . (0) . . m Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications (Tom moved page Paper:Mittag-Leffler Functions and Their Applications/H.J. Haubold to Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications)
- 21:08, 2 January 2018 (diff | hist) . . (+80) . . N Paper:Mittag-Leffler Functions and Their Applications/H.J. Haubold (Tom moved page Paper:Mittag-Leffler Functions and Their Applications/H.J. Haubold to Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications) (current)
- 17:31, 2 January 2018 (diff | hist) . . (+197) . . Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications
- 16:49, 2 January 2018 (diff | hist) . . (+146) . . N Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications (Created page with "{{Book|Mittag-Leffler Functions and Their Applications|2011|Journal of Applied Mathematics||H.J. Haubold|author2=A.M. Mathai|author3=R.K. Saxena}}")
- 16:47, 2 January 2018 (diff | hist) . . (+89) . . Mittag-Leffler
- 15:54, 2 January 2018 (diff | hist) . . (+274) . . N Mittag-Leffler (Created page with "The Mittag-Leffler function $E_{\alpha, \beta}$ is defined by the series $$E_{\alpha, \beta}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{\Gamma(\alpha k + \beta)},$$ where...")
- 15:53, 2 January 2018 (diff | hist) . . (+25) . . Main Page (→Special functions)
- 14:42, 23 December 2017 (diff | hist) . . (+81) . . Paper:Harvey Dubner/Factorial and Primorial Primes (current)
- 14:36, 23 December 2017 (diff | hist) . . (+194) . . N Primorial (Created page with "The primorial $p_n\#$ of the prime number $p_n$ is $$p_n\#=p_n p_{n-1} p_{n-2} \ldots p_1.$$ =References= * {{PaperReference|Factorial and Primorial Primes|1987|Harvey D...") (current)
- 06:18, 23 December 2017 (diff | hist) . . (-1) . . Paper:Harvey Dubner/Factorial and Primorial Primes
- 06:18, 23 December 2017 (diff | hist) . . (+152) . . N Paper:Harvey Dubner/Factorial and Primorial Primes (Created page with "{{Book|Factorial and Primorial Primes|1987|Journal of Recreational Mathematics||Harvey Dubner}} ===Contents==== Primorial<br /> Category:Paper")
- 05:25, 21 December 2017 (diff | hist) . . (+482) . . N Gamma'(z)/Gamma(z)=-gamma-1/z+Sum z/(k(z+k)) (Created page with "==Theorem== The following formula holds: $$\dfrac{\Gamma'(z)}{\Gamma(z)} = -\gamma-\dfrac{1}{z}+\displaystyle\sum_{k=1}^{\infty} \dfrac{z}{k(z+k)},$$ where $\Gamma$ denotes ...") (current)
- 05:22, 21 December 2017 (diff | hist) . . (+55) . . Gamma
- 05:19, 21 December 2017 (diff | hist) . . (+63) . . Book:Earl David Rainville/Special Functions (current)
- 05:18, 21 December 2017 (diff | hist) . . (+97) . . Reciprocal gamma written as an infinite product
- 05:10, 21 December 2017 (diff | hist) . . (+11) . . Fresnel C (current)
- 05:10, 21 December 2017 (diff | hist) . . (0) . . Fresnel C
- 05:08, 21 December 2017 (diff | hist) . . (+277) . . Book:Milton Abramowitz/Handbook of mathematical functions (current)
- 05:06, 21 December 2017 (diff | hist) . . (+440) . . N Integral of (z^n)log(z)dz=(z^(n+1)/(n+1))log(z)-z^(n+1)/(n+1)^2 for integer n neq -1 (Created page with "==Theorem== The following formula holds for integers $n \neq -1$: $$\displaystyle\int z^n \log(z) \mathrm{d}z= \dfrac{z^{n+1}\log(z)}{n+1} - \dfrac{z^{n+1}}{(n+1)^2},$$ where...")
- 05:05, 21 December 2017 (diff | hist) . . (+458) . . N Antiderivative of the logarithm (Created page with "==Theorem== The following formula holds: $$\displaystyle\int \log(z) \mathrm{d}z = z\log(z)-z+C,$$ where $\log$ denotes the logarithm. ==Proof== ==References== * {{BookR...") (current)
- 05:03, 21 December 2017 (diff | hist) . . (+25) . . Logarithm (current)
- 05:02, 21 December 2017 (diff | hist) . . (+157) . . Logarithm
- 05:01, 21 December 2017 (diff | hist) . . (+384) . . N Nth derivative of logarithm (Created page with "==Theorem== The following formula holds: $$\dfrac{\mathrm{d}^n}{\mathrm{d}z^n} \log(z)=(-1)^{n-1}(n-1)! z^{-n},$$ where $\log$ denotes the logarithm. ==Proof== ==Referen...") (current)
- 04:59, 21 December 2017 (diff | hist) . . (+21) . . Derivative of the logarithm (current)
- 04:57, 21 December 2017 (diff | hist) . . (+136) . . Derivative of the logarithm
- 04:56, 21 December 2017 (diff | hist) . . (+1) . . Log((1+z)/(1-z)) as continued fraction (current)
- 04:54, 21 December 2017 (diff | hist) . . (+53) . . Elliptic E (current)
- 04:52, 21 December 2017 (diff | hist) . . (+104) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 04:52, 21 December 2017 (diff | hist) . . (+453) . . N E(m)=(pi/2)2F1(-1/2,1/2;1;m) (Created page with "==Theorem== The following formula holds: $$E(m) = \dfrac{\pi}{2} {}_2F_1 \left( - \dfrac{1}{2}, \dfrac{1}{2};1;m \right),$$ where $E$ denotes Elliptic E, $\pi$ denotes p...") (current)
- 04:50, 21 December 2017 (diff | hist) . . (+452) . . N K(m)=(pi/2)2F1(1/2,1/2;1;m) (Created page with "==Theorem== The following formula holds: $$K(m)=\dfrac{\pi}{2} {}_2F_1 \left( \dfrac{1}{2}, \dfrac{1}{2}; 1; m \right),$$ where $K$ denotes Elliptic K, $\pi$ denotes [[pi]...") (current)
- 04:48, 21 December 2017 (diff | hist) . . (+52) . . Elliptic K (current)
- 04:47, 21 December 2017 (diff | hist) . . (+27) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 04:47, 21 December 2017 (diff | hist) . . (-18) . . Elliptic K
- 03:37, 21 December 2017 (diff | hist) . . (+9) . . Laplace transform (current)
- 03:27, 21 December 2017 (diff | hist) . . (+2) . . Laplace transform
- 03:23, 21 December 2017 (diff | hist) . . (+1) . . Laplace transform
- 02:41, 21 December 2017 (diff | hist) . . (+1) . . Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) (current)
- 02:40, 21 December 2017 (diff | hist) . . (+515) . . N Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) (Created page with "==Theorem== The following formula holds: $$\mathrm{Li}_2(z)+\mathrm{Li}_2(1-z)=\dfrac{\pi^2}{6} - \log(z)\log(1-z),$$ where $\mathrm{Li}_2$ denotes the dilogarithm, $\pi$...")
- 02:33, 21 December 2017 (diff | hist) . . (+33) . . Dilogarithm (→References)
- 02:27, 21 December 2017 (diff | hist) . . (+37) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 02:26, 21 December 2017 (diff | hist) . . (+293) . . Dilogarithm
- 01:58, 21 December 2017 (diff | hist) . . (+104) . . Euler totient (→Videos) (current)
- 01:09, 21 December 2017 (diff | hist) . . (+284) . . Struve function (current)
- 01:08, 21 December 2017 (diff | hist) . . (+40) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 01:07, 21 December 2017 (diff | hist) . . (-16) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 01:05, 21 December 2017 (diff | hist) . . (-2) . . H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0 (current)
- 01:05, 21 December 2017 (diff | hist) . . (+563) . . N H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z) (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_{\frac{3}{2}}(z)=\sqrt{\dfrac{z}{2\pi}} \left( 1 + \dfrac{2}{z^2} \right)- \sqrt{\dfrac{2}{\pi z}} \left( \sin(z)+ \dfrac...") (current)
- 01:03, 21 December 2017 (diff | hist) . . (0) . . m H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) (Tom moved page H (1/2)(z)=(2/(pi z))^(1/2)(1-cos(z)) to H (1/2)(z)=sqrt(2/(pi z))(1-cos(z))) (current)
- 01:03, 21 December 2017 (diff | hist) . . (+49) . . N H (1/2)(z)=(2/(pi z))^(1/2)(1-cos(z)) (Tom moved page H (1/2)(z)=(2/(pi z))^(1/2)(1-cos(z)) to H (1/2)(z)=sqrt(2/(pi z))(1-cos(z))) (current)
- 01:03, 21 December 2017 (diff | hist) . . (+543) . . N H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_{\frac{1}{2}}(z) = \sqrt{\dfrac{2}{\pi z}}(1-\cos(z)),$$ where $\mathbf{H}_{\frac{1}{2}}$ denotes a Struve function,...")
- 00:59, 21 December 2017 (diff | hist) . . (+466) . . N H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0 (Created page with "==Theorem== If $n \geq 0$ is an integer, then $$\mathbf{H}_{-(n+\frac{1}{2})}(z) = (-1)^n J_{n+\frac{1}{2}}(z),$$ where $\mathbf{H}$ denotes a Struve function and $J$ deno...")
- 00:57, 21 December 2017 (diff | hist) . . (+55) . . H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 (current)
- 00:56, 21 December 2017 (diff | hist) . . (+423) . . N H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 (Created page with "==Theorem== The following formula holds for $x>0$ and $\nu \geq \dfrac{1}{2}$: $$\mathbf{H}_{\nu}(x) \geq 0,$$ where $\mathbf{H}$ denotes a Struve function. ==Proof== ==...")
- 00:55, 21 December 2017 (diff | hist) . . (+525) . . N D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1) (Created page with "==Theorem== The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \left[ z^{-\nu}\mathbf{H}_{\nu}(z) \right] = \dfrac{1}{\sqrt{\pi}2^{\nu}\Gamma(\nu+\frac{3}{2})} - z...") (current)
- 00:51, 21 December 2017 (diff | hist) . . (-34) . . Derivative of Struve H0 (current)
- 00:50, 21 December 2017 (diff | hist) . . (0) . . m D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) (Tom moved page D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1) to D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) without leaving a redirect) (current)
- 00:50, 21 December 2017 (diff | hist) . . (+484) . . N D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) (Created page with "==Theorem== The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \left[ z^{\nu}\mathbf{H}_{\nu}(z) \right]=z^{\nu}\mathbf{H}_{\nu-1}(z),$$ where $\mathbf{H}$ denotes...")
- 00:47, 21 December 2017 (diff | hist) . . (+17) . . Derivative of Struve H0
- 00:47, 21 December 2017 (diff | hist) . . (+78) . . Struve function (→Properties)
- 01:50, 20 December 2017 (diff | hist) . . (-22) . . Main Page
- 01:49, 20 December 2017 (diff | hist) . . (0) . . Clausen cosine
- 01:46, 20 December 2017 (diff | hist) . . (+297) . . N Unsigned Lah numbers (Created page with "The unsigned Lah numbers $L(n,k)$ are defined by $$L(n,k)={{n-1} \choose {k-1}} \dfrac{n!}{k!},$$ where ${{n-1} \choose {k-1}}$ denotes a binomial coefficient and $n!$ den...") (current)
- 01:46, 20 December 2017 (diff | hist) . . (+7) . . Signed Lah numbers (current)
- 01:46, 20 December 2017 (diff | hist) . . (+43) . . Signed Lah numbers
- 01:45, 20 December 2017 (diff | hist) . . (+254) . . N Signed Lah numbers (Created page with "The signed Lah numbers $L(n,k)$ are defined by $$L(n,k)={{n-1} \choose {k-1}} \dfrac{n!}{k!},$$ where ${{n-1} \choose {k-1}}$ denotes a binomial coefficient and $n!$ denot...")
- 01:44, 20 December 2017 (diff | hist) . . (+38) . . Main Page (→Special sequences)
- 01:32, 20 December 2017 (diff | hist) . . (+250) . . N Matrix exponential (Created page with "The $n$-dimensional matrix exponential $\exp_n \colon \mathbb{R}^{n \times n} \rightarrow \mathbb{R}^{n \times n}$ is defined by $$\exp_n(X)=\displaystyle\sum_{k=0}^{\infty} \...")
- 01:29, 20 December 2017 (diff | hist) . . (+245) . . N C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x) (Created page with "==Theorem== The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} C_n^{\lambda}(x)=2\lambda C_{n+1}^{\lambda+1}(x),$$ where $C_n^{\lambda}$ denotes Gegenbauer C....") (current)
- 01:29, 20 December 2017 (diff | hist) . . (-5) . . Gegenbauer C (→Properties) (current)
- 01:28, 20 December 2017 (diff | hist) . . (-207) . . Gegenbauer C
- 01:28, 20 December 2017 (diff | hist) . . (+260) . . N NC n^(lambda)(x)=(n-1+2lambda)xC (n-1)^(lambda)(x)-2lambda(1-x^2)C (n-2)^(lambda-1)(x) (Created page with "==Theorem== The following formula holds: $$nC_n^{\lambda}(x) = (n-1+2\lambda)xC_{n-1}^{\lambda}(x) - 2\lambda(1-x^2)C_{n-2}^{\lambda-1}(x),$$ where $C_n^{\lambda}$ denotes G...") (current)
- 01:27, 20 December 2017 (diff | hist) . . (-212) . . Gegenbauer C
- 01:26, 20 December 2017 (diff | hist) . . (+11) . . Gegenbauer C
- 01:26, 20 December 2017 (diff | hist) . . (+13) . . (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x)) (current)
- 01:26, 20 December 2017 (diff | hist) . . (+248) . . N (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x)) (Created page with "==Theorem== The following formula holds: $$(n+2\lambda)C_n^{\lambda}(x) = 2\lambda(C_n^{\lambda+1}(x)-xC_{n-1}^{\lambda+1}(x)),$$ where $C_n^{\lambda}$ denotes [[Gegenbauer C]...")
- 01:25, 20 December 2017 (diff | hist) . . (-211) . . Gegenbauer C (→Properties)
- 01:24, 20 December 2017 (diff | hist) . . (+11) . . Gegenbauer C
- 23:49, 19 December 2017 (diff | hist) . . (+1) . . Gegenbauer C (→Properties)
- 23:48, 19 December 2017 (diff | hist) . . (0) . . m NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x)) (Tom moved page NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x) to NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x))) (current)
- 23:48, 19 December 2017 (diff | hist) . . (+84) . . N NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x) (Tom moved page NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x) to NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x))) (current)
- 23:48, 19 December 2017 (diff | hist) . . (+243) . . N NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x)) (Created page with "==Theorem== The following formula holds: $$nC_n^{\lambda}(x) = 2\lambda(xC_{n-1}^{\lambda+1}(x) - C_{n-2}^{\lambda+1}(x)),$$ where $C_n^{\lambda}$ denotes Gegenbauer C. =...")
- 23:47, 19 December 2017 (diff | hist) . . (-213) . . Gegenbauer C (→Properties)
- 23:47, 19 December 2017 (diff | hist) . . (+259) . . N (n+2)C (n+2)^(lambda)(x)=2(lambda+n+1)xC (n+1)^(lambda)(x)-(2lambda+n)C n^(lambda)(x) (Created page with "==Theorem== The following formula holds: $$(n+2)C_{n+2}^{\lambda}(x)=2(\lambda+n+1)xC_{n+1}^{\lambda}(x)-(2\lambda+n)C_n^{\lambda}(x),$$ where $C_{n+2}^{\lambda}$ denotes Ge...") (current)
- 23:46, 19 December 2017 (diff | hist) . . (-209) . . Gegenbauer C (→Properties)
- 23:45, 19 December 2017 (diff | hist) . . (+490) . . N Orthogonality of Gegenbauer C on (-1,1) (Created page with "==Theorem== The following formula holds: $$\displaystyle\int_{-1}^1 (1-x^2)^{\lambda-\frac{1}{2}} C_n^{\lambda}(x)C_m^{\lambda}(x) \mathrm{d}x = \left\{ \begin{array}{ll} 0, &...") (current)
- 23:42, 19 December 2017 (diff | hist) . . (-1,017) . . Gegenbauer C
- 23:37, 19 December 2017 (diff | hist) . . (+3,881) . . N Book:W.W. Bell/Special Functions for Scientists and Engineers (Created page with "{{Book|Special Functions for Scientists and Engineers|1968|D. Van Nostrand||W.W. Bell}} ===Contents=== :PREFACE :LIST OF SYMBOLS :Chapter 1 Series Solution of Differential Eq...")
- 23:24, 19 December 2017 (diff | hist) . . (+3,652) . . N Book:Richard Beals/Special functions, a graduate text (Created page with "{{Book|Special functions, a graduate text|2010|Cambridge University Press||Richard Beals|author2=Roderick Wong}} ===Contents=== :1 Orientation ::1.1 Power series solutions ::...")
- 22:54, 19 December 2017 (diff | hist) . . (+19) . . Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition (current)
- 22:52, 19 December 2017 (diff | hist) . . (+81) . . Book:T.S. Chihara/An Introduction to Orthogonal Polynomials (current)
- 22:52, 19 December 2017 (diff | hist) . . (+32) . . Orthogonality relation for cosine on (0,pi) (current)
- 22:50, 19 December 2017 (diff | hist) . . (+9) . . Orthogonality of Chebyshev U on (-1,1) (current)
- 22:49, 19 December 2017 (diff | hist) . . (-72) . . Relationship between Chebyshev U and Gegenbauer C (current)
- 22:43, 19 December 2017 (diff | hist) . . (-82) . . Relationship between Chebyshev U and hypergeometric 2F1 (current)
- 22:42, 19 December 2017 (diff | hist) . . (+383) . . N Orthogonality of Chebyshev U on (-1,1) (Created page with "==Theorem== The following formula holds for $m, n \in \{0,1,2,\ldots\}$: $$\int_{-1}^1 \dfrac{U_m(x)U_n(x)}{\sqrt{1-x^2}} dx = \left\{ \begin{array}{ll} 0 &; m \neq n \\ \dfra...")
- 22:40, 19 December 2017 (diff | hist) . . (-264) . . Chebyshev U
- 22:38, 19 December 2017 (diff | hist) . . (+248) . . Chebyshev T
- 22:36, 19 December 2017 (diff | hist) . . (+203) . . Orthogonality of Chebyshev T on (-1,1) (current)
- 22:33, 19 December 2017 (diff | hist) . . (-11) . . Relationship between Chebyshev T and Gegenbauer C (current)
- 22:33, 19 December 2017 (diff | hist) . . (-71) . . Relationship between Chebyshev T and Gegenbauer C
- 22:32, 19 December 2017 (diff | hist) . . (+28) . . Relationship between Chebyshev T and hypergeometric 2F1 (current)
- 22:32, 19 December 2017 (diff | hist) . . (-107) . . Relationship between Chebyshev T and hypergeometric 2F1
- 22:31, 19 December 2017 (diff | hist) . . (-4) . . Chebyshev T
- 22:30, 19 December 2017 (diff | hist) . . (+18) . . Chebyshev T (→Properties)
- 22:30, 19 December 2017 (diff | hist) . . (+1) . . Orthogonality of Chebyshev T on (-1,1)
- 22:30, 19 December 2017 (diff | hist) . . (+9) . . Orthogonality of Chebyshev T on (-1,1)
- 22:30, 19 December 2017 (diff | hist) . . (+382) . . N Orthogonality of Chebyshev T on (-1,1) (Created page with "==Theorem== The following formula holds for $m,n \in \{0,1,2,\ldots\}$: $$\int_{-1}^1 \dfrac{T_m(x)T_n(x)}{\sqrt{1-x^2}} dx = \left\{ \begin{array}{ll} 0 &; m \neq n \\ \dfrac...")
- 22:15, 19 December 2017 (diff | hist) . . (-346) . . Chebyshev T (→Properties)
- 22:14, 19 December 2017 (diff | hist) . . (+77) . . T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (current)
- 22:13, 19 December 2017 (diff | hist) . . (+170) . . N T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (Created page with "==Theorem== The following formula holds for $n=0,1,2,\ldots$: $$T_{n+1}(x)-2xT_n(x)+T_{n-1}(x)=0.$$ ==Proof== ==References== Category:Theorem Category:Unproven")
- 22:13, 19 December 2017 (diff | hist) . . (0) . . Chebyshev T (→Properties)
- 22:12, 19 December 2017 (diff | hist) . . (-466) . . Chebyshev T
- 22:10, 19 December 2017 (diff | hist) . . (+114) . . Book:T.S. Chihara/An Introduction to Orthogonal Polynomials
- 22:09, 19 December 2017 (diff | hist) . . (+54) . . Cosine (current)
- 22:09, 19 December 2017 (diff | hist) . . (+33) . . Orthogonality relation for cosine on (0,pi)
- 22:08, 19 December 2017 (diff | hist) . . (+364) . . N Orthogonality relation for cosine on (0,pi) (Created page with "==Theorem== The following formula holds for $m,n \in \{0,1,2,\ldots\}$ with $m\neq n$: $$\displaystyle\int_0^{\pi} \cos(mt)\cos(nt) \mathrm{d}t=0.$$ ==Proof== ==References==...")
- 22:07, 19 December 2017 (diff | hist) . . (+361) . . N 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) (Created page with "==Theorem== The following formula holds for $m,n \in \{0,1,2,\ldots\}$: $$2\cos(mt)\cos(nt)=\cos((m+n)t)+\cos((m-n)t),$$ where $\cos$ denotes cosine. ==Proof== ==Referen...") (current)
- 22:03, 19 December 2017 (diff | hist) . . (+50) . . Cosine
- 22:02, 19 December 2017 (diff | hist) . . (+2,060) . . N Book:T.S. Chihara/An Introduction to Orthogonal Polynomials (Created page with "{{Book|An Introduction to Orthogonal Polynomials|1978|Gordon and Breach||T.S. Chihara}} === Contents === :PREFACE :CHAPTER I. ELEMENTARY THEORY OF ORTHOGONAL POLYNOMIALS ::1...")
- 20:06, 14 December 2017 (diff | hist) . . (-31) . . Main Page (→Special functions)
- 20:00, 14 December 2017 (diff | hist) . . (0) . . File:Signumglyph.png (Tom uploaded a new version of File:Signumglyph.png) (current)
- 19:59, 14 December 2017 (diff | hist) . . (0) . . File:Signumglyph.png (Tom uploaded a new version of File:Signumglyph.png)
- 19:52, 14 December 2017 (diff | hist) . . (-1) . . Signum (replaced image with correct one for sgn(x))
- 19:51, 14 December 2017 (diff | hist) . . (+732) . . N File:Signumplot.png (<pre> #!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 10, 10 x1=np.arange(-4,-0.05,0.01); x2=np.arange(0.05,4,0.01); def g1(x): return -1 def g2(x):...) (current)
- 01:54, 26 November 2017 (diff | hist) . . (+196) . . Bernstein B (current)
- 01:13, 26 November 2017 (diff | hist) . . (+22) . . Bernstein B (→External links)
- 01:13, 26 November 2017 (diff | hist) . . (+129) . . Bernstein B
- 01:11, 26 November 2017 (diff | hist) . . (+211) . . N Bernstein B (Created page with "The Bernstein polynomials $B_k^n(x)$ are defined by $$B_k^n(x)={n \choose k} x^k (1-x)^{n-k},$$ where ${n \choose k}$ denotes a Binomial coefficient. =Properties= =Refer...")
- 12:22, 7 November 2017 (diff | hist) . . (-7) . . Main Page (→Polynomials)
- 12:22, 7 November 2017 (diff | hist) . . (+7) . . Main Page (→Polynomials)
- 12:22, 7 November 2017 (diff | hist) . . (+22) . . Main Page (→Polynomials)
- 19:55, 4 November 2017 (diff | hist) . . (+304) . . Struve function
- 19:53, 4 November 2017 (diff | hist) . . (+1) . . Integral representation of Struve function (3) (current)
- 16:29, 4 November 2017 (diff | hist) . . (+438) . . N Derivative of Struve H0 (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_0'(z) = \dfrac{2}{\pi} - \mathbf{H}_1(z),$$ where $\mathbf{H}$ denotes the Struve function. ==Proof== ==References=...")
- 16:27, 4 November 2017 (diff | hist) . . (+549) . . N Recurrence relation for Struve function (2) (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_{\nu-1}(z)-\mathbf{H}_{\nu+1}(z) = 2\mathbf{H}_{\nu}'(z) - \dfrac{z^{\nu}}{2^{\nu}\sqrt{\pi}\Gamma(\nu+\frac{3}{2})},$$ w...") (current)
- 16:26, 4 November 2017 (diff | hist) . . (+43) . . Recurrence relation for Struve fuction (current)
- 16:25, 4 November 2017 (diff | hist) . . (+547) . . N Recurrence relation for Struve fuction (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_{\nu-1}(z)+\mathbf{H}_{\nu+1}(z) = \dfrac{2\nu}{z} \mathbf{H}_{\nu}(z) + \dfrac{z^{\nu}}{2^{\nu}\sqrt{\pi}\Gamma(\nu+\fra...")
- 16:23, 4 November 2017 (diff | hist) . . (+560) . . Integral representation of Struve function (3)
- 16:17, 4 November 2017 (diff | hist) . . (+252) . . N Integral representation of Struve function (3) (Created page with "==Theorem== ==Proof== ==References== * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral representation of Stru...")
- 16:14, 4 November 2017 (diff | hist) . . (+699) . . N Integral representation of Struve function (2) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(\nu)>-\dfrac{1}{2}$: $$\mathbf{H}_{\nu}(z) = \dfrac{z^{\nu}}{2^{\nu-1}\sqrt{\pi}\Gamma(\nu+\frac{1}{2})} \displaystyle...") (current)
- 16:11, 4 November 2017 (diff | hist) . . (+1) . . Integral representation of Struve function (current)
- 16:11, 4 November 2017 (diff | hist) . . (+632) . . N Integral representation of Struve function (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(\nu) > - \dfrac{1}{2}$: $$\mathbf{H}_{\nu}(z) = \dfrac{z^{\nu}}{2^{\nu-1}\sqrt{\pi}\Gamma(\nu+\frac{1}{2})} \displayst...")
- 22:58, 31 October 2017 (diff | hist) . . (+803) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 22:40, 31 October 2017 (diff | hist) . . (+32) . . Struve function
- 01:15, 29 October 2017 (diff | hist) . . (+775) . . Main Page
- 00:28, 29 October 2017 (diff | hist) . . (+123) . . Main Page (→Error function and friends)
- 00:27, 29 October 2017 (diff | hist) . . (+847) . . N File:Dawsondplusglyph.png (<pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams import scipy.special rcParams['figure.figsize'] = 2.4,2.4 x1=np.arange(-15,15,0.001) f=np.vectorize(lambda x: scipy.special.dawsn...) (current)
- 00:21, 29 October 2017 (diff | hist) . . (+105) . . Dawson D+ (current)
- 00:20, 29 October 2017 (diff | hist) . . (+518) . . N File:Dawsondplusplot.png (Category:Plot <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams import scipy.special rcParams['figure.figsize'] = 10, 10 x=np.arange(-15,15,0.001); f=np.vectorize(lambda x: sc...) (current)
- 00:12, 29 October 2017 (diff | hist) . . (-1) . . Dawson D- (current)
- 00:12, 29 October 2017 (diff | hist) . . (+9) . . Dawson D+
- 00:11, 29 October 2017 (diff | hist) . . (-118) . . Clausen sine
- 00:03, 29 October 2017 (diff | hist) . . (0) . . Clausen sine
- 00:01, 29 October 2017 (diff | hist) . . (+118) . . Clausen sine
- 23:00, 28 October 2017 (diff | hist) . . (+4,594) . . N Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition (Created page with "__NOTOC__ {{Book|Formulas and Theorems for the Special Functions of Mathematical Physics |1966|Springer-Verlag||Wilhelm Magnus|author2 = Fritz Oberhettinger|author3=Raj Pal S...")
- 22:01, 28 October 2017 (diff | hist) . . (+1) . . Main Page (→Bessel functions and friends)
- 22:00, 28 October 2017 (diff | hist) . . (+125) . . Main Page (→Bessel functions and friends)
- 21:59, 28 October 2017 (diff | hist) . . (+24) . . File:Struveh2glyph.png (current)
- 21:59, 28 October 2017 (diff | hist) . . (0) . . N File:Struveh2glyph.png
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