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- 19:45, 11 June 2016 (diff | hist) . . (+443) . . N Value of derivative of trigamma at positive integer plus 1/2 (Created page with "==Theorem== The following formula holds: $$\psi^{(m)} \left( n + \dfrac{1}{2} \right)=\dfrac{\pi^2}{2} - 4 \displaystyle\sum_{k=1}^n \dfrac{1}{(2k-1)^2},$$ where $\psi^{(m)}$...")
- 19:43, 11 June 2016 (diff | hist) . . (+47) . . Value of polygamma at 1/2
- 19:42, 11 June 2016 (diff | hist) . . (+512) . . N Value of polygamma at 1/2 (Created page with "==Theorem== The following formula holds for $m=1,2,3,\ldots$: $$\psi^{(m)} \left( \dfrac{1}{2} \right) = (-1)^{m+1} m! \left( 2^{m+1}-1 \right) \zeta(m+1),$$ where $\psi^{(m)}...")
- 19:39, 11 June 2016 (diff | hist) . . (+44) . . Value of polygamma at positive integer
- 19:38, 11 June 2016 (diff | hist) . . (+488) . . N Value of polygamma at positive integer (Created page with "==Theorem== The following formula holds: $$\psi^{(m)}(n+1)=(-1)^m m! \left[ -\zeta(m+1)+1 + \dfrac{1}{2^{m+1}}+\ldots + \dfrac{1}{n^{m+1}} \right],$$ where $\psi^{(m)}$ denote...")
- 19:34, 11 June 2016 (diff | hist) . . (+105) . . Value of polygamma at 1
- 08:08, 11 June 2016 (diff | hist) . . (-1) . . Value of polygamma at 1
- 08:08, 11 June 2016 (diff | hist) . . (+21) . . Value of polygamma at 1
- 08:08, 11 June 2016 (diff | hist) . . (+355) . . N Value of polygamma at 1 (Created page with "==Theorem== The following formula holds: $$\psi^{(m)}(1)=(-1)^{m+1} m! \zeta(m+1),$$ where $\psi^{(m)}$ denotes the polygamma, $m!$ denotes the factorial$, and $\zeta$...")
- 08:06, 11 June 2016 (diff | hist) . . (+153) . . Integral representation of polygamma for Re(z) greater than 0
- 08:05, 11 June 2016 (diff | hist) . . (0) . . Polygamma
- 08:04, 11 June 2016 (diff | hist) . . (0) . . m Integral representation of polygamma for Re(z) greater than 0 (Tom moved page Integral representation of polygamma to Integral representation of polygamma for Re(z) greater than 0)
- 08:04, 11 June 2016 (diff | hist) . . (+75) . . N Integral representation of polygamma (Tom moved page Integral representation of polygamma to Integral representation of polygamma for Re(z) greater than 0) (current)
- 08:04, 11 June 2016 (diff | hist) . . (-70) . . Polygamma
- 07:05, 11 June 2016 (diff | hist) . . (+272) . . Polygamma
- 06:34, 11 June 2016 (diff | hist) . . (-76) . . Relation between polygamma and Hurwitz zeta (current)
- 06:34, 11 June 2016 (diff | hist) . . (-112) . . Polygamma series representation (current)
- 06:33, 11 June 2016 (diff | hist) . . (-110) . . Polygamma reflection formula
- 06:32, 11 June 2016 (diff | hist) . . (-110) . . Polygamma recurrence relation
- 06:32, 11 June 2016 (diff | hist) . . (-119) . . Integral representation of polygamma 2 (current)
- 06:31, 11 June 2016 (diff | hist) . . (-117) . . Integral representation of polygamma for Re(z) greater than 0
- 06:30, 11 June 2016 (diff | hist) . . (+30) . . Polygamma
- 06:22, 11 June 2016 (diff | hist) . . (-9) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 06:20, 11 June 2016 (diff | hist) . . (+835) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 05:54, 11 June 2016 (diff | hist) . . (+340) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 05:53, 11 June 2016 (diff | hist) . . (0) . . Bessel Y
- 04:54, 11 June 2016 (diff | hist) . . (+44) . . Relationship between Bessel Y sub n and Bessel Y sub -n (current)
- 04:54, 11 June 2016 (diff | hist) . . (+377) . . N Relationship between Bessel Y sub n and Bessel Y sub -n (Created page with "==Theorem== The following formula holds for $n \in \mathbb{Z}$: $$Y_{-n}(z)=(-1)^n Y_n(z),$$ where $Y_{-n}$ denotes the Bessel function of the second kind. ==Pro...")
- 04:52, 11 June 2016 (diff | hist) . . (+455) . . N Relationship between Bessel J sub n and Bessel J sub -n (Created page with "==Theorem== The following formula holds for $n \in \mathbb{Z}$, $$J_{-n}(z)=(-1)^n J_n(z),$$ where $J_{-n}$ denotes the Bessel function of the first kind. ==Proo...") (current)
- 04:50, 11 June 2016 (diff | hist) . . (+55) . . Hankel H (2) in terms of csc and Bessel J (current)
- 04:47, 11 June 2016 (diff | hist) . . (+609) . . N Hankel H (2) in terms of csc and Bessel J (Created page with "==Theorem== The following formula holds: $$H_{\nu}^{(2)}(z)=i\csc(\nu \pi) \left[ J_{-\nu}(z)-e^{\nu \pi i}J_{\nu}(z) \right],$$ where $H_{\nu}^{(2)}$ denotes the Hankel H (...")
- 04:12, 11 June 2016 (diff | hist) . . (-14) . . Hankel H (2)
- 04:12, 11 June 2016 (diff | hist) . . (+200) . . Hankel H (2)
- 04:09, 11 June 2016 (diff | hist) . . (+646) . . N Hankel H (1) in terms of csc and Bessel J (Created page with "==Theorem== The following formula holds: $$H_{\nu}^{(1)}(z)=i \csc(\nu \pi) \left[ e^{-\nu \pi i} J_{\nu}(z)-J_{-\nu}(z) \right],$$ where $H_{\nu}^{(1)}$ denotes the Hankel...") (current)
- 04:02, 11 June 2016 (diff | hist) . . (-17) . . Hankel H (1)
- 04:01, 11 June 2016 (diff | hist) . . (+139) . . Bessel Y
- 04:01, 11 June 2016 (diff | hist) . . (+184) . . Hankel H (1)
- 03:51, 11 June 2016 (diff | hist) . . (+2) . . Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition
- 03:49, 11 June 2016 (diff | hist) . . (+672) . . Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition
- 03:37, 11 June 2016 (diff | hist) . . (+157) . . Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition
- 03:35, 11 June 2016 (diff | hist) . . (+5) . . Differential equation for Jacobi P
- 03:35, 11 June 2016 (diff | hist) . . (+410) . . N Differential equation for Jacobi P (Created page with "==Theorem== The Jacobi P polynomials $y(x)=P_n^{(\alpha,\beta)}(x)$ satisfy the differential equation $$(1-x^2)y''(x)+[\beta-\alpha-(\alpha+\beta+2)x]y'(x)+n(n+\alpha+\bet...")
- 03:30, 11 June 2016 (diff | hist) . . (+45) . . Jacobi P (current)
- 03:28, 11 June 2016 (diff | hist) . . (-1,174) . . Jacobi P
- 03:28, 11 June 2016 (diff | hist) . . (-2) . . Jacobi P (→References)
- 03:27, 11 June 2016 (diff | hist) . . (+134) . . Jacobi P
- 03:23, 11 June 2016 (diff | hist) . . (+201) . . Jacobi P
- 02:34, 11 June 2016 (diff | hist) . . (+437) . . Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition
- 01:46, 11 June 2016 (diff | hist) . . (+9) . . Orthogonal polynomials footer
- 01:45, 11 June 2016 (diff | hist) . . (+8) . . Orthogonal polynomials footer
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