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- 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)
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