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- 19:42, 15 March 2018 (diff | hist) . . (0) . . m Gamma(z+1)=zGamma(z) (Tom moved page Factorial property of gamma to Gamma(z+1)=zGamma(z): Gamma(z+1)=zGamma(z))
- 19:42, 15 March 2018 (diff | hist) . . (+34) . . N Factorial property of gamma (Tom moved page Factorial property of gamma to Gamma(z+1)=zGamma(z): Gamma(z+1)=zGamma(z)) (current)
- 19:41, 15 March 2018 (diff | hist) . . (-7) . . Gamma (→Properties)
- 19:41, 15 March 2018 (diff | hist) . . (+185) . . Gamma(1)=1
- 19:40, 15 March 2018 (diff | hist) . . (0) . . m Gamma(1)=1 (Tom moved page Value of Gamma(1) to Gamma(1)=1)
- 19:40, 15 March 2018 (diff | hist) . . (+24) . . N Value of Gamma(1) (Tom moved page Value of Gamma(1) to Gamma(1)=1) (current)
- 19:40, 15 March 2018 (diff | hist) . . (+125) . . Beta
- 19:39, 15 March 2018 (diff | hist) . . (+113) . . Gamma
- 19:34, 15 March 2018 (diff | hist) . . (+331) . . Book:W.W. Bell/Special Functions for Scientists and Engineers
- 19:33, 15 March 2018 (diff | hist) . . (+67) . . Chebyshev T (current)
- 19:33, 15 March 2018 (diff | hist) . . (+69) . . Chebyshev U (current)
- 19:32, 15 March 2018 (diff | hist) . . (+66) . . Chebyshev T
- 19:32, 15 March 2018 (diff | hist) . . (+75) . . Chebyshev U
- 19:32, 15 March 2018 (diff | hist) . . (+530) . . N U n(x)=Sum (-1)^k n!/((2k+1)!(n-2k-1)!)(1-x^2)^(k+1/2)x^(n-2k-1) (Created page with "==Theorem== The following formula holds: $$U_n(x) = \displaystyle\sum_{k=0}^{\left\lfloor \frac{n-1}{2} \right\rfloor} \dfrac{(-1)^k n!}{(2k+1)!(n-2k-1)!} (1-x^2)^{k+\frac{1}{...") (current)
- 19:28, 15 March 2018 (diff | hist) . . (+58) . . T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) (current)
- 19:26, 15 March 2018 (diff | hist) . . (+508) . . N T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) (Created page with "==Theorem== The following formula holds: $$T_n(x) = \displaystyle\sum_{k=0}^{\left\lfloor \frac{n}{2} \right\rfloor} \dfrac{(-1)^k n!}{(2k)!(n-2k)!} (1-x^2)^k x^{n-2k},$$ wher...")
- 19:22, 15 March 2018 (diff | hist) . . (+1) . . U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (current)
- 19:22, 15 March 2018 (diff | hist) . . (-2) . . U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n
- 19:21, 15 March 2018 (diff | hist) . . (+50) . . U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n
- 19:20, 15 March 2018 (diff | hist) . . (+476) . . N U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (Created page with "==Theorem== The following formula holds: $$U_n(x) =-\dfrac{i}{2} \left[ \left( x + i \sqrt{1-x^2} \right)^n + \left( x-i\sqrt{1-x^2} \right)^n \right],$$ where $U_n$ denotes [...")
- 19:18, 15 March 2018 (diff | hist) . . (+456) . . N T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n (Created page with "==Theorem== The following formula holds: $$T_n(x)=\dfrac{\left(x+i\sqrt{1-x^2} \right)^n+\left(x-i\sqrt{1-x^2} \right)^n}{2},$$ where $T_n$ denotes Chebyshev T and $i$ den...") (current)
- 19:15, 15 March 2018 (diff | hist) . . (+50) . . Chebyshev U
- 19:01, 15 March 2018 (diff | hist) . . (+54) . . Book:W.W. Bell/Special Functions for Scientists and Engineers
- 19:00, 15 March 2018 (diff | hist) . . (+120) . . Chebyshev U
- 19:00, 15 March 2018 (diff | hist) . . (+120) . . Chebyshev T
- 14:42, 15 March 2018 (diff | hist) . . (+34) . . Book:W.W. Bell/Special Functions for Scientists and Engineers
- 14:42, 15 March 2018 (diff | hist) . . (+115) . . Hypergeometric pFq (current)
- 14:39, 15 March 2018 (diff | hist) . . (+214) . . Book:W.W. Bell/Special Functions for Scientists and Engineers
- 14:37, 15 March 2018 (diff | hist) . . (-433) . . Laguerre L (current)
- 14:36, 15 March 2018 (diff | hist) . . (+348) . . N L n'(x)=-Sum L k(x) (Created page with "==Theorem== The following formula holds: $$L_n'(x) = -\displaystyle\sum_{k=0}^{n-1} L_k(x),$$ where $L_n$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|...") (current)
- 14:35, 15 March 2018 (diff | hist) . . (+356) . . N XL n'(x)=nL n(x)-n L (n-1)(x) (Created page with "==Theorem== The following formula holds: $$xL_n'(x)=nL_n(x)-nL_{n-1}(x),$$ where $L_n$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|Special Functions f...") (current)
- 14:32, 15 March 2018 (diff | hist) . . (+23) . . (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (current)
- 14:32, 15 March 2018 (diff | hist) . . (+343) . . N (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (Created page with "==Theorem== The following formula holds: $$(n+1)L_{n+1}(x)=(2n+1-x)L_n(x)-nL_{n-1}(x),$$ where $L_{n+1}$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|S...")
- 14:30, 15 March 2018 (diff | hist) . . (+38) . . Orthogonality of Laguerre L (current)
- 14:30, 15 March 2018 (diff | hist) . . (-202) . . Laguerre L (→Properties)
- 14:28, 15 March 2018 (diff | hist) . . (+249) . . Book:W.W. Bell/Special Functions for Scientists and Engineers
- 14:22, 15 March 2018 (diff | hist) . . (-285) . . Laguerre L
- 14:21, 15 March 2018 (diff | hist) . . (+323) . . N Kronecker delta (Created page with "The Kronecker delta is the function $\delta \colon \mathbb{N}_0 \times \mathbb{N}_0 \rightarrow \{0,1\}$ defined by $$\delta(m,n)=\left\{ \begin{array}{ll} 0, & \quad m \neq n...") (current)
- 14:19, 15 March 2018 (diff | hist) . . (+431) . . N Orthogonality of Laguerre L (Created page with "==Theorem== The following formula holds: $$\displaystyle\int_0^{\infty} e^{-x} L_n(x) L_m(x) \mathrm{d}x = \delta_{mn},$$ where $e^{-x}$ denotes the exponential, $L_n$ den...")
- 14:18, 15 March 2018 (diff | hist) . . (+21) . . L n'(0)=-n (current)
- 14:17, 15 March 2018 (diff | hist) . . (+289) . . N L n'(0)=-n (Created page with "==Theorem== The following formula holds: $$L_n'(0)=-n,$$ where $L_n$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|Special Functions for Scientists and...")
- 14:17, 15 March 2018 (diff | hist) . . (+319) . . N L n(0)=1 (Created page with "==Theorem== The following formula holds: $$L_n(0)=1,$$ where $L_n$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|Special Functions for Scientists and En...") (current)
- 14:15, 15 March 2018 (diff | hist) . . (+2) . . L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x)) (current)
- 14:14, 15 March 2018 (diff | hist) . . (+18) . . L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x))
- 14:09, 15 March 2018 (diff | hist) . . (+402) . . N L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x)) (Created page with "==Theorem== The following formula holds: $$L_n(x) = \dfrac{e^x}{n!} \dfrac{d^n}{dx^n} (x^n e^{-x}),$$ where $L_n$ denotes Laguerre L and $e^x$ denotes the exponential...")
- 14:08, 15 March 2018 (diff | hist) . . (-224) . . Laguerre L (→Properties)
- 14:08, 15 March 2018 (diff | hist) . . (-1) . . Generating function for Laguerre L (current)
- 14:07, 15 March 2018 (diff | hist) . . (+445) . . N Generating function for Laguerre L (Created page with "==Theorem== The following formula holds: $$\dfrac{e^{\frac{-xt}{1-t}}}{1-t} = \displaystyle\sum_{k=0}^{\infty} L_k(x)t^k,$$ where $e^{\frac{-xt}{1-t}}$ denotes an exponentia...")
- 14:06, 15 March 2018 (diff | hist) . . (+28) . . Laguerre L
- 13:46, 15 March 2018 (diff | hist) . . (-246) . . Laguerre L (→Properties)
- 13:45, 15 March 2018 (diff | hist) . . (+115) . . Laguerre L
- 13:45, 15 March 2018 (diff | hist) . . (0) . . m Book:W.W. Bell/Special Functions for Scientists and Engineers (Tom moved page Book:Special Functions for Scientists and Engineers/W.W. Bell to Book:W.W. Bell/Special Functions for Scientists and Engineers: Book:W.W. Bell/Special Functions for Scientists and Engineers)
- 13:45, 15 March 2018 (diff | hist) . . (+75) . . N Book:Special Functions for Scientists and Engineers/W.W. Bell (Tom moved page Book:Special Functions for Scientists and Engineers/W.W. Bell to Book:W.W. Bell/Special Functions for Scientists and Engineers: Book:W.W. Bell/Special Functions for Scientists and Engineers) (current)
- 13:42, 15 March 2018 (diff | hist) . . (+11) . . Laguerre L
- 13:41, 15 March 2018 (diff | hist) . . (-97) . . Laguerre L
- 13:39, 15 March 2018 (diff | hist) . . (+62) . . Laguerre L
- 13:38, 15 March 2018 (diff | hist) . . (+57) . . Associated Laguerre L (current)
- 03:35, 12 March 2018 (diff | hist) . . (+107) . . Arcsin cdf (current)
- 03:33, 12 March 2018 (diff | hist) . . (+351) . . N Continuous uniform cdf (Created page with "The continuous uniform cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is given by $$F(x) = \left\{ \begin{array}{ll} 0, & \quad x<a \\ \dfra...") (current)
- 03:31, 12 March 2018 (diff | hist) . . (+266) . . N Continuous uniform pdf (Created page with "The continuous uniform probability density function $f \colon [a,b] \rightarrow \mathbb{R}$ where $a,b \in \mathbb{R}$ is defined by $$f(x) = \dfrac{1}{b-a}.$$ =Propertie...") (current)
- 03:29, 12 March 2018 (diff | hist) . . (+11) . . Main Page (→Cumulative Density Functions)
- 03:29, 12 March 2018 (diff | hist) . . (+11) . . Main Page (→Probability density funcitons)
- 03:26, 12 March 2018 (diff | hist) . . (+16) . . Normal cdf (current)
- 03:26, 12 March 2018 (diff | hist) . . (+428) . . N Normal cdf (Created page with "The normal cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $\sigma^2 >0$ by $$F(x) = \dfrac{1}{2} \le...")
- 03:22, 12 March 2018 (diff | hist) . . (+401) . . N Normal pdf (Created page with "The normal probability density function $f \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $\sigma^2>0$ by $$f(x)=\dfrac{1}{\sqrt{2\pi\si...") (current)
- 03:18, 12 March 2018 (diff | hist) . . (+22) . . Laplace pdf (→See also) (current)
- 03:17, 12 March 2018 (diff | hist) . . (+313) . . N Laplace pdf (Created page with "The Laplace probability density function $f \colon \mathbb{R} \rightarrow \mathbb{R}$ for $\mu \in \mathbb{R}$ and $b>0$ by $$f(x) = \dfrac{1}{2b} \exp \left(-\dfrac{|x-\m...")
- 03:16, 12 March 2018 (diff | hist) . . (-4) . . Laplace cdf (→See also) (current)
- 03:15, 12 March 2018 (diff | hist) . . (+503) . . N Laplace cdf (Created page with "The Laplace cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $b>0$ and is given by $$F(x) = \left\{ \b...")
- 03:11, 12 March 2018 (diff | hist) . . (+294) . . N Exponential cdf (Created page with "The exponential cumulative distribution function $F \colon [0,\infty) \rightarrow \mathbb{R}$ is given by $$F(x)=1-e^{-\lambda x},$$ where $e^{-\lambda x}$ denotes the ...") (current)
- 03:10, 12 March 2018 (diff | hist) . . (+314) . . N Exponential pdf (Created page with "The exponential probability density function $f \colon [0,\infty) \rightarrow \mathbb{R}$ is defined for $\lambda >0$ by $$f(x)=\lambda e^{-\lambda x},$$ where $e^{\lambd...") (current)
- 15:46, 9 March 2018 (diff | hist) . . (+6) . . Main Page (→Cumulative Density Functions)
- 15:45, 9 March 2018 (diff | hist) . . (+309) . . N Arcsin cdf (Created page with "The arcsin cumulative distribution function $F \colon [0,1] \rightarrow \mathbb{R}$ is given by $$F(x) = \dfrac{2}{\pi} \arcsin\left(\sqrt{x} \right),$$ where $\pi$ denot...")
- 15:44, 9 March 2018 (diff | hist) . . (+255) . . N Arcsin pdf (Created page with "The arcsin probability density function $f \colon [0,1] \rightarrow \mathbb{R}$ is given by $$f(x) = \dfrac{1}{\pi \sqrt{x(1-x)}},$$ where $\pi$ denotes pi. =Properti...") (current)
- 15:41, 9 March 2018 (diff | hist) . . (+393) . . N Cauchy cdf (Created page with "The Cauchy cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ for $x_0 \in \mathbb{R}$ and $\gamma > 0$ is given by $$F(x) = \dfrac{1}{\pi} \mat...") (current)
- 15:39, 9 March 2018 (diff | hist) . . (+33) . . Cauchy pdf (current)
- 15:38, 9 March 2018 (diff | hist) . . (+317) . . N Cauchy pdf (Created page with "The Cauchy probability density function $f \colon \mathbb{R} \rightarrow \mathbb{R}$ for $x_0 \in \mathbb{R}$ and $\gamma >0$ is given by $$f(x) = \dfrac{1}{\pi \gamma \le...")
- 15:36, 9 March 2018 (diff | hist) . . (+214) . . Main Page (→Continuous distributions)
- 15:32, 9 March 2018 (diff | hist) . . (+38) . . Main Page (→Continuous distributions)
- 06:07, 4 March 2018 (diff | hist) . . (+173) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I (current)
- 06:05, 4 March 2018 (diff | hist) . . (+592) . . N Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) (Created page with "==Theorem== The following formula holds for $|z|<\pi$: $$z \mathrm{coth}(z) = 2 \displaystyle\sum_{k=0}^{\infty} (-1)^{k+1} \zeta(2k) \dfrac{z^{2k}}{\pi^{2k}},$$ where $\mathr...") (current)
- 06:03, 4 March 2018 (diff | hist) . . (+49) . . Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (current)
- 06:01, 4 March 2018 (diff | hist) . . (+583) . . N Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (Created page with "==Theorem== The following formula holds for $|z| < \pi$: $$z \mathrm{coth}(z) = \displaystyle\sum_{k=0}^{\infty} 2^{2k} B_{2k} \dfrac{z^{2k}}{(2k)!},$$ where $\mathrm{coth}$...")
- 05:57, 4 March 2018 (diff | hist) . . (+515) . . N Z coth(z) = 2z/(e^(2z)-1) + z (Created page with "==Theorem== The following formula holds for $|z|<\pi$: $$z \mathrm{coth}(z) = z+\dfrac{2z}{e^{2z}-1},$$ where $\mathrm{coth} denotes hyperbolic cotangent and $e^{2z}$...") (current)
- 05:53, 4 March 2018 (diff | hist) . . (+161) . . Coth (→Properties) (current)
- 05:47, 4 March 2018 (diff | hist) . . (+21) . . Bateman F
- 05:44, 4 March 2018 (diff | hist) . . (+4) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 05:44, 4 March 2018 (diff | hist) . . (+4) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume II (current)
- 05:44, 4 March 2018 (diff | hist) . . (+4) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume III (current)
- 05:43, 4 March 2018 (diff | hist) . . (0) . . m Book:Arthur Erdélyi/Higher Transcendental Functions Volume III (Tom moved page Book:Harry Bateman/Higher Transcendental Functions Volume III to Book:Arthur Erdélyi/Higher Transcendental Functions Volume III)
- 05:43, 4 March 2018 (diff | hist) . . (+77) . . N Book:Harry Bateman/Higher Transcendental Functions Volume III (Tom moved page Book:Harry Bateman/Higher Transcendental Functions Volume III to Book:Arthur Erdélyi/Higher Transcendental Functions Volume III) (current)
- 05:43, 4 March 2018 (diff | hist) . . (+82) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume III
- 05:42, 4 March 2018 (diff | hist) . . (+82) . . Kelvin kei (current)
- 05:42, 4 March 2018 (diff | hist) . . (+82) . . Kelvin bei (current)
- 05:42, 4 March 2018 (diff | hist) . . (+82) . . Kelvin ker (current)
- 05:41, 4 March 2018 (diff | hist) . . (+82) . . Kelvin ber (current)
- 05:41, 4 March 2018 (diff | hist) . . (+82) . . Bessel J (current)
- 05:40, 4 March 2018 (diff | hist) . . (0) . . m Book:Arthur Erdélyi/Higher Transcendental Functions Volume II (Tom moved page Book:Harry Bateman/Higher Transcendental Functions Volume II to Book:Arthur Erdélyi/Higher Transcendental Functions Volume II)
- 05:40, 4 March 2018 (diff | hist) . . (+76) . . N Book:Harry Bateman/Higher Transcendental Functions Volume II (Tom moved page Book:Harry Bateman/Higher Transcendental Functions Volume II to Book:Arthur Erdélyi/Higher Transcendental Functions Volume II) (current)
- 05:40, 4 March 2018 (diff | hist) . . (+82) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume II
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