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- 15:21, 18 December 2023 (diff | hist) . . (-1) . . Book:Thomas Ernst/A Comprehensive Treatment of q-Calculus (current)
- 15:19, 18 December 2023 (diff | hist) . . (+2) . . Book:Thomas Ernst/A Comprehensive Treatment of q-Calculus
- 00:50, 13 September 2023 (diff | hist) . . (+37) . . Integral representation of Airy Ai (current)
- 00:50, 13 September 2023 (diff | hist) . . (+13) . . Integral representation of Airy Ai
- 00:49, 13 September 2023 (diff | hist) . . (+13) . . Integral representation of Airy Ai
- 15:47, 26 August 2023 (diff | hist) . . (+40) . . Main Page (→Special constants) (current)
- 15:45, 26 August 2023 (diff | hist) . . (+26) . . Transcendental (current)
- 15:44, 26 August 2023 (diff | hist) . . (0) . . m Transcendental (Tom moved page Transcendental number to Transcendental)
- 15:44, 26 August 2023 (diff | hist) . . (+28) . . N Transcendental number (Tom moved page Transcendental number to Transcendental) (current)
- 15:44, 26 August 2023 (diff | hist) . . (+107) . . N Algebraic (Created page with "A number is called algebraic if it is the solution of a polynomial equation. =See also= Transcendental") (current)
- 15:44, 26 August 2023 (diff | hist) . . (+25) . . Transcendental
- 15:43, 26 August 2023 (diff | hist) . . (+4) . . Transcendental
- 18:26, 13 July 2023 (diff | hist) . . (-3) . . Main Page (→External Links)
- 19:44, 7 September 2020 (diff | hist) . . (-4) . . Clausen sine (current)
- 19:44, 7 September 2020 (diff | hist) . . (+108) . . Clausen sine
- 19:43, 7 September 2020 (diff | hist) . . (+290) . . N File:Clausensine0.5.png (from mpmath import * import numpy as np import matplotlib.pyplot as plt mp.dps=25; mp.pretty = True cplot(lambda x: clsin(0.5,x),[-10,10],[-5,5],points=50000,verbose=True) plt.title(r'Domain coloring of $Cl_{0.5}(z)$.') plt.savefig('clausensine0.5.pn...) (current)
- 18:56, 7 September 2020 (diff | hist) . . (+136) . . Clausen cosine (current)
- 18:55, 7 September 2020 (diff | hist) . . (+297) . . N File:Clausencosine0.5plot.png (from mpmath import * import numpy as np import matplotlib.pyplot as plt mp.dps=25; mp.pretty = True cplot(lambda x: clcos(0.5,x),[-10,10],[-10,10],points=50000,verbose=True) plt.title(r'Domain coloring of $\tilde{Cl}_{0.5}(z)$.') plt.savefig('clausen...) (current)
- 11:57, 10 October 2019 (diff | hist) . . (+61) . . Bateman F (current)
- 11:55, 10 October 2019 (diff | hist) . . (+124) . . N Paper:Harry Bateman/The Polynomial Fn(x) (Created page with "{{Book|The Polynomial $F_n(x)$|1934|Annals of Mathematics Second Series||Harry Bateman}} ===Contents=== Category:Paper") (current)
- 11:51, 10 October 2019 (diff | hist) . . (+442) . . N Orthogonality of Bateman F on R (Created page with "==Theorem== The following formula holds: $$\displaystyle\int_{-\infty}^{\infty} F_m(it)F_n(it) \mathrm{sech}^2\left(\dfrac{\pi t}{2} \right)\mathrm{d}t = \dfrac{4(-1)^n}{\pi (...") (current)
- 11:48, 10 October 2019 (diff | hist) . . (+42) . . Bateman F (→Properties)
- 11:47, 10 October 2019 (diff | hist) . . (+334) . . Bateman F
- 01:30, 3 August 2019 (diff | hist) . . (+517) . . N Paper:Lucas Jódar/On the hypergeometric matrix function (Created page with "{{Book|On the hypergeometric matrix function|1998|Journal of Computational and Applied Mathematics||Lucas Jódar}} ===Contents=== (1) <br /> ---------------...") (current)
- 01:05, 3 August 2019 (diff | hist) . . (+327) . . Main Page (→Matrix functions)
- 12:16, 8 June 2019 (diff | hist) . . (+51) . . Main Page (→Special constants)
- 00:48, 4 January 2019 (diff | hist) . . (+1) . . Main Page (→Special sequences)
- 00:47, 4 January 2019 (diff | hist) . . (+28) . . Main Page (→Special sequences)
- 01:14, 25 December 2018 (diff | hist) . . (+35) . . Q-shifted factorial (current)
- 15:38, 22 December 2018 (diff | hist) . . (+1,888) . . N Book:Charalambos Charalambides/Discrete q-Distributions (Created page with "{{Book|Discrete q-Distributions|2016|Wiley|9781119119043|Charalambos Charalambides}} === Contents === :Preface :1 Basic $q$-Combinatorics and $q$-Hypergeometric Series ::1.1...") (current)
- 13:12, 1 August 2018 (diff | hist) . . (+133) . . Paper:David Zeitlin/On Identities for Fibonacci Numbers (current)
- 13:12, 1 August 2018 (diff | hist) . . (+133) . . Fibonacci numbers (→Properties) (current)
- 13:09, 1 August 2018 (diff | hist) . . (-73) . . Fibonacci numbers (→References)
- 13:09, 1 August 2018 (diff | hist) . . (+73) . . Fibonacci numbers (→References)
- 13:08, 1 August 2018 (diff | hist) . . (+15) . . Paper:David Zeitlin/On Identities for Fibonacci Numbers
- 13:08, 1 August 2018 (diff | hist) . . (+132) . . N Paper:David Zeitlin/On Identities for Fibonacci Numbers (Created page with "{{Book|On Identities for Fibonacci Numbers|1963|The American Mathematical Monthly||David Zeitlin}} [[Fibonacci [[Category:Paper]]")
- 13:07, 1 August 2018 (diff | hist) . . (+76) . . Fibonacci numbers
- 02:58, 15 July 2018 (diff | hist) . . (+698) . . Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition (→Contents) (current)
- 18:24, 16 June 2018 (diff | hist) . . (+53) . . Lambert W (current)
- 18:23, 16 June 2018 (diff | hist) . . (+216) . . Lambert W
- 18:23, 16 June 2018 (diff | hist) . . (-1) . . Paper:R. M. Corless/On the Lambert W function (current)
- 18:22, 16 June 2018 (diff | hist) . . (+210) . . N Paper:R. M. Corless/On the Lambert W function (Created page with "{{Book|On the Lambert W function|1996|Advances in Computational Mathematics||Rob M. Corless|author2=G. H. Gonnet|author3=D.E.G. Hare|author4=D.J. Jeffrey|author5=D.E. Knuth}}...")
- 18:12, 16 June 2018 (diff | hist) . . (+61) . . Book:Richard Beals/Special functions, a graduate text (current)
- 18:12, 16 June 2018 (diff | hist) . . (+130) . . Gamma(z+1)=zGamma(z) (current)
- 18:12, 16 June 2018 (diff | hist) . . (-13) . . Gamma (current)
- 18:11, 16 June 2018 (diff | hist) . . (+14) . . Gamma (→References)
- 18:10, 16 June 2018 (diff | hist) . . (+132) . . Gamma
- 18:10, 16 June 2018 (diff | hist) . . (0) . . m Book:Richard Beals/Special functions, a graduate text (Tom moved page Book:Special functions, a graduate text/Richard Beals to Book:Richard Beals/Special functions, a graduate text)
- 18:10, 16 June 2018 (diff | hist) . . (+67) . . N Book:Special functions, a graduate text/Richard Beals (Tom moved page Book:Special functions, a graduate text/Richard Beals to Book:Richard Beals/Special functions, a graduate text) (current)
- 01:27, 18 April 2018 (diff | hist) . . (+25) . . Main Page
- 11:54, 5 April 2018 (diff | hist) . . (-5) . . Gamma (→Properties)
- 11:54, 5 April 2018 (diff | hist) . . (0) . . m Gamma(z)Gamma(1-z)=pi/sin(pi z) (Tom moved page Euler's reflection formula for gamma to Gamma(z)Gamma(1-z)=pi/sin(pi z)) (current)
- 11:54, 5 April 2018 (diff | hist) . . (+45) . . N Euler's reflection formula for gamma (Tom moved page Euler's reflection formula for gamma to Gamma(z)Gamma(1-z)=pi/sin(pi z)) (current)
- 11:54, 5 April 2018 (diff | hist) . . (+17) . . Gamma (→Properties)
- 11:53, 5 April 2018 (diff | hist) . . (+184) . . Gamma(z+1)=zGamma(z)
- 11:53, 5 April 2018 (diff | hist) . . (+14) . . Gamma (→References)
- 11:52, 5 April 2018 (diff | hist) . . (-7) . . Gamma (→Properties)
- 11:52, 5 April 2018 (diff | hist) . . (+185) . . Gamma
- 00:20, 5 April 2018 (diff | hist) . . (+6,583) . . N Book:Roelof Koekoek/Hypergeometric Orthogonal Polynomials and Their q-Analogues (Created page with "__NOTOC__ {{Book|Hypergeometric Orthogonal Polynomials and Their q-Analogues|2010|Springer Verlag||Roelof Koekoek|author2=Peter A. Lesky|author3=René F. Swarttouw}} ===Cont...") (current)
- 00:41, 28 March 2018 (diff | hist) . . (+19) . . File:Struveplots.png (current)
- 00:48, 25 March 2018 (diff | hist) . . (+15) . . Main Page (→*-integral functions)
- 00:47, 25 March 2018 (diff | hist) . . (0) . . m Entire exponential integral (Tom moved page Ein function to Entire exponential integral) (current)
- 00:47, 25 March 2018 (diff | hist) . . (+41) . . N Ein function (Tom moved page Ein function to Entire exponential integral) (current)
- 01:26, 24 March 2018 (diff | hist) . . (+338) . . N Bickley-Naylor (Created page with "The Bickely-Naylor functions $\mathrm{Ki}_n$ are defined by $$\mathrm{Ki}_n(x) = \displaystyle\int_0^{\frac{\pi}{2}} e^{-\frac{x}{\sin(\theta)}}\sin^{n-1}(\theta) \mathrm{d}\t...") (current)
- 01:24, 24 March 2018 (diff | hist) . . (+25) . . Main Page (→Special functions)
- 00:48, 24 March 2018 (diff | hist) . . (+38) . . Exponential integral Ei (current)
- 00:48, 24 March 2018 (diff | hist) . . (+67) . . Ei(x)=-Integral from -x to infinity of e^(-t)/t dt (current)
- 00:47, 24 March 2018 (diff | hist) . . (+3) . . Ei(x)=-Integral from -x to infinity of e^(-t)/t dt
- 00:47, 24 March 2018 (diff | hist) . . (+10) . . Ei(x)=-Integral from -x to infinity of e^(-t)/t dt
- 00:46, 24 March 2018 (diff | hist) . . (+64) . . N Ei(-x)=-Integral from -x to infinity of e^(-t)/t dt (Tom moved page Ei(-x)=-Integral from -x to infinity of e^(-t)/t dt to Ei(x)=-Integral from -x to infinity of e^(-t)/t dt) (current)
- 00:46, 24 March 2018 (diff | hist) . . (0) . . m Ei(x)=-Integral from -x to infinity of e^(-t)/t dt (Tom moved page Ei(-x)=-Integral from -x to infinity of e^(-t)/t dt to Ei(x)=-Integral from -x to infinity of e^(-t)/t dt)
- 00:46, 24 March 2018 (diff | hist) . . (-1) . . Ei(x)=-Integral from -x to infinity of e^(-t)/t dt
- 00:45, 24 March 2018 (diff | hist) . . (+28) . . Exponential integral E (current)
- 00:44, 24 March 2018 (diff | hist) . . (-29) . . Ei(x)=-Integral from -x to infinity of e^(-t)/t dt
- 00:43, 24 March 2018 (diff | hist) . . (+295) . . Ei(x)=-Integral from -x to infinity of e^(-t)/t dt
- 00:43, 24 March 2018 (diff | hist) . . (+28) . . Exponential integral Ei (→References)
- 00:42, 24 March 2018 (diff | hist) . . (+1) . . Exponential integral Ei (→Properties)
- 00:41, 24 March 2018 (diff | hist) . . (+3) . . Ei(x)=-Integral from -x to infinity of e^(-t)/t dt
- 00:41, 24 March 2018 (diff | hist) . . (0) . . m Ei(x)=-Integral from -x to infinity of e^(-t)/t dt (Tom moved page Ei(-x)=-Integral from x to infinity of e^(-t)/t dt to Ei(-x)=-Integral from -x to infinity of e^(-t)/t dt)
- 00:41, 24 March 2018 (diff | hist) . . (+65) . . N Ei(-x)=-Integral from x to infinity of e^(-t)/t dt (Tom moved page Ei(-x)=-Integral from x to infinity of e^(-t)/t dt to Ei(-x)=-Integral from -x to infinity of e^(-t)/t dt) (current)
- 00:38, 24 March 2018 (diff | hist) . . (+71) . . Exponential integral Ei
- 00:05, 24 March 2018 (diff | hist) . . (+114) . . Exponential integral E (→References)
- 03:36, 17 March 2018 (diff | hist) . . (+210) . . Paper:James Whitbread Lee Glaisher/On certain definite integrals involving the exponential-integral (current)
- 03:34, 17 March 2018 (diff | hist) . . (+238) . . Relationship between logarithmic integral and exponential integral (current)
- 03:33, 17 March 2018 (diff | hist) . . (+228) . . Logarithmic integral (current)
- 03:31, 17 March 2018 (diff | hist) . . (+14) . . Exponential integral Ei series (current)
- 03:31, 17 March 2018 (diff | hist) . . (+258) . . Exponential integral Ei series
- 03:30, 17 March 2018 (diff | hist) . . (+1) . . Ei(x)=-Integral from -x to infinity of e^(-t)/t dt
- 03:29, 17 March 2018 (diff | hist) . . (+480) . . N Ei(x)=-Integral from -x to infinity of e^(-t)/t dt (Created page with "==Theorem== The following formula holds: $$\mathrm{Ei}(-x) = -\displaystyle\int_x^{\infty} \dfrac{e^{-t}}{t} \mathrm{d}t,$$ where $\mathrm{Ei}$ denotes the exponential integ...")
- 03:27, 17 March 2018 (diff | hist) . . (+44) . . Exponential integral Ei
- 03:26, 17 March 2018 (diff | hist) . . (-12) . . Exponential integral Ei (→Properties)
- 19:50, 15 March 2018 (diff | hist) . . (+144) . . Book:W.W. Bell/Special Functions for Scientists and Engineers (current)
- 19:49, 15 March 2018 (diff | hist) . . (-7) . . Beta (current)
- 19:47, 15 March 2018 (diff | hist) . . (+4) . . Gamma(1)=1 (current)
- 19:47, 15 March 2018 (diff | hist) . . (+4) . . Gamma(z+1)=zGamma(z)
- 19:47, 15 March 2018 (diff | hist) . . (+132) . . Gamma(n+1)=n! (current)
- 19:46, 15 March 2018 (diff | hist) . . (+26) . . Gamma(z+1)=zGamma(z)
- 19:46, 15 March 2018 (diff | hist) . . (0) . . m Gamma(n+1)=n! (Tom moved page Gamma at positive integers to Gamma(n+1)=n!)
- 19:46, 15 March 2018 (diff | hist) . . (+27) . . N Gamma at positive integers (Tom moved page Gamma at positive integers to Gamma(n+1)=n!) (current)
- 19:44, 15 March 2018 (diff | hist) . . (0) . . Gamma(1)=1
- 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
- 05:39, 4 March 2018 (diff | hist) . . (0) . . m Book:Norman L. Johnson/Continuous Univariate Distributions Volume 2/Second Edition (Tom moved page Creating Book:Norman L. Johnson/Continuous Univariate Distributions Volume 2/Second Edition to Book:Norman L. Johnson/Continuous Univariate Distributions Volume 2/Second Edition without leaving a redirect) (current)
- 01:24, 4 March 2018 (diff | hist) . . (+175) . . N Book:Norman L. Johnson/Continuous Univariate Distributions Volume 2/Second Edition (Created page with "{{Book|Continuous Univariate Distributions Volume 2|1995|John Wiley & Sons, Inc||Norman L. Johnson|author2=Samuel Kotz|author3=N. Balakrishnan}} =Contents= Category:Book")
- 01:08, 4 March 2018 (diff | hist) . . (+102) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 01:07, 4 March 2018 (diff | hist) . . (+401) . . N Euler E n'(x)=nE n-1(x) (Created page with "==Theorem== The following formula holds: $$E_n'(x)=n E_{n-1}(x),$$ where $E_n$ denotes an Euler polynomial. ==References== * {{BookReference|Higher Transcendental...") (current)
- 01:05, 4 March 2018 (diff | hist) . . (+17) . . Euler E generating function (current)
- 01:05, 4 March 2018 (diff | hist) . . (-193) . . Euler E (→Properties) (current)
- 01:04, 4 March 2018 (diff | hist) . . (+14) . . Euler E generating function
- 01:04, 4 March 2018 (diff | hist) . . (+11) . . Euler numbers (current)
- 01:03, 4 March 2018 (diff | hist) . . (+208) . . Euler E generating function
- 01:03, 4 March 2018 (diff | hist) . . (+511) . . N Euler numbers (Created page with "The Euler numbers $E_k$ are the coefficients in the following Taylor series for $|z| < \dfrac{\pi}{2}$: $$\mathrm{sech}(z) = \displaystyle\sum_{k=0}^{\infty} E_k \dfrac{z^...")
- 23:27, 3 March 2018 (diff | hist) . . (+82) . . Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (current)
- 23:27, 3 March 2018 (diff | hist) . . (+82) . . 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) (current)
- 23:26, 3 March 2018 (diff | hist) . . (+82) . . (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k) (current)
- 23:26, 3 March 2018 (diff | hist) . . (+82) . . 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) (current)
- 23:26, 3 March 2018 (diff | hist) . . (+82) . . 1Phi0(a;;z) as infinite product (current)
- 23:26, 3 March 2018 (diff | hist) . . (+82) . . Basic hypergeometric phi (current)
- 23:26, 3 March 2018 (diff | hist) . . (+82) . . Q-shifted factorial
- 23:26, 3 March 2018 (diff | hist) . . (+82) . . 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) (current)
- 23:25, 3 March 2018 (diff | hist) . . (+82) . . 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4) (current)
- 23:25, 3 March 2018 (diff | hist) . . (+82) . . 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) (current)
- 23:25, 3 March 2018 (diff | hist) . . (+82) . . 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) (current)
- 23:25, 3 March 2018 (diff | hist) . . (+82) . . 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z) (current)
- 23:25, 3 March 2018 (diff | hist) . . (+82) . . 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z) (current)
- 23:25, 3 March 2018 (diff | hist) . . (+82) . . Pochhammer symbol with non-negative integer subscript (current)
- 23:25, 3 March 2018 (diff | hist) . . (+164) . . Pochhammer (current)
- 23:25, 3 March 2018 (diff | hist) . . (+164) . . Hypergeometric pFq
- 23:24, 3 March 2018 (diff | hist) . . (+82) . . (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0 (current)
- 23:24, 3 March 2018 (diff | hist) . . (+82) . . (c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0 (current)
- 23:24, 3 March 2018 (diff | hist) . . (+82) . . C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0 (current)
- 23:24, 3 March 2018 (diff | hist) . . (+82) . . (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0 (current)
- 23:23, 3 March 2018 (diff | hist) . . (+82) . . (b-a)2F1+a2F1(a+1)-b2F1(b+1)=0 (current)
- 23:23, 3 March 2018 (diff | hist) . . (+82) . . (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0 (current)
- 23:23, 3 March 2018 (diff | hist) . . (+164) . . Hypergeometric 2F1 (current)
- 23:23, 3 March 2018 (diff | hist) . . (+82) . . Bernoulli numbers (current)
- 23:23, 3 March 2018 (diff | hist) . . (+82) . . Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (current)
- 23:23, 3 March 2018 (diff | hist) . . (+82) . . Li2(z)=zPhi(z,2,1) (current)
- 23:23, 3 March 2018 (diff | hist) . . (+82) . . Relationship between dilogarithm and log(1-z)/z (current)
- 23:22, 3 March 2018 (diff | hist) . . (+82) . . Dilogarithm (current)
- 23:22, 3 March 2018 (diff | hist) . . (+82) . . Lerch transcendent (current)
- 23:22, 3 March 2018 (diff | hist) . . (+82) . . Digamma at z+n (current)
- 23:22, 3 March 2018 (diff | hist) . . (+82) . . Digamma at n+1 (current)
- 23:22, 3 March 2018 (diff | hist) . . (+82) . . Digamma functional equation (current)
- 23:22, 3 March 2018 (diff | hist) . . (+82) . . Digamma at 1 (current)
- 23:21, 3 March 2018 (diff | hist) . . (+82) . . Digamma (current)
- 21:04, 3 March 2018 (diff | hist) . . (+82) . . Beta in terms of sine and cosine (current)
- 21:04, 3 March 2018 (diff | hist) . . (+82) . . Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (current)
- 21:03, 3 March 2018 (diff | hist) . . (+82) . . Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (current)
- 21:03, 3 March 2018 (diff | hist) . . (+82) . . Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (current)
- 21:03, 3 March 2018 (diff | hist) . . (+82) . . 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) (current)
- 21:03, 3 March 2018 (diff | hist) . . (+82) . . 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) (current)
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