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Evaluating Elliptic Integrals in terms of Gamma Function

score 744 · Answer 1 · 2026-03-26 22:17:30

744

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Evaluating Elliptic Integrals in terms of Gamma Function

Published on 26 Mar 2026 - 22:17

score 84 · Answer 2 · 2026-03-31 10:15:35

84

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How to get to this equality $\prod_{m=1}^{\infty} \frac{m+1}{m}\times\frac{m+x}{m+x+1}=x+1$?

Published on 31 Mar 2026 - 10:15

score 804 · Answer 3 · 2015-08-18 21:39:22

804

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Approximation of the Gamma function

Published on 18 Aug 2015 - 21:39

score 4.7k · Answer 4 · 2015-08-20 13:39:42

4.7k

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Lower and upper bound of the Stirling's approximation

Published on 20 Aug 2015 - 13:39

score 1k · Answer 5 · 2015-08-21 08:23:01

1k

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Intuition behind $(-\frac{1}{2})! = \sqrt{\pi}$

Published on 21 Aug 2015 - 8:23

score 211 · Answer 6 · 2015-08-22 22:46:50

211

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Yet another Gamma function approximation

Published on 22 Aug 2015 - 22:46

score 138 · Answer 7 · 2015-08-25 09:32:08

138

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How to calculate $\displaystyle \lim_{\alpha \to -1}\left(2\Gamma(-\alpha-1)+\Gamma\left(\frac{\alpha + 1}{2}\right) \right)$

Published on 25 Aug 2015 - 9:32

score 878 · Answer 8 · 2026-03-26 02:54:03

878

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Proof of Functional Equation Zeta

Published on 26 Mar 2026 - 2:54

score 77 · Answer 9 · 2026-03-28 09:55:31

77

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A Question from Murray - Asymptotic Analysis

Published on 28 Mar 2026 - 9:55

score 4.3k · Answer 10 · 2015-09-03 10:35:17

4.3k

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Simplify division of two gamma functions

Published on 03 Sep 2015 - 10:35

score 1.4k · Answer 11 · 2026-03-26 12:40:39

1.4k

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If $1\leq \alpha$ show show that the gamma density has a maximum at $\frac{\alpha - 1}{\lambda} $

Published on 26 Mar 2026 - 12:40

score 1k · Answer 12 · 2015-09-09 00:27:46

1k

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Looking to solve an integral of the form $\int_1^\infty (y-1)^{n-1} y^{-n} e^{(\alpha -\alpha n)\frac{(y-1) }{y}} \; dy$

Published on 09 Sep 2015 - 0:27

score 140 · Answer 13 · 2026-04-01 20:03:07

140

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Integrating $\int_{0}^{\infty}\prod_{k=1}^{n}(kx-1)e^{-ax} {d}x,$ where $a$ and $n$ are parameters.

Published on 01 Apr 2026 - 20:03

score 218 · Answer 14 · 2015-09-11 23:23:18

218

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Limit involving Gamma function

Published on 11 Sep 2015 - 23:23

score 135 · Answer 15 · 2015-09-15 00:24:32

135

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Integral in terms of gamma

Published on 15 Sep 2015 - 0:24

List Question

Evaluating Elliptic Integrals in terms of Gamma Function

How to get to this equality $\prod_{m=1}^{\infty} \frac{m+1}{m}\times\frac{m+x}{m+x+1}=x+1$?

Approximation of the Gamma function

Lower and upper bound of the Stirling's approximation

Intuition behind $(-\frac{1}{2})! = \sqrt{\pi}$

Yet another Gamma function approximation

How to calculate $\displaystyle \lim_{\alpha \to -1}\left(2\Gamma(-\alpha-1)+\Gamma\left(\frac{\alpha + 1}{2}\right) \right)$

Proof of Functional Equation Zeta

A Question from Murray - Asymptotic Analysis

Simplify division of two gamma functions

If $1\leq \alpha$ show show that the gamma density has a maximum at $\frac{\alpha - 1}{\lambda} $

Looking to solve an integral of the form $\int_1^\infty (y-1)^{n-1} y^{-n} e^{(\alpha -\alpha n)\frac{(y-1) }{y}} \; dy$

Integrating $\int_{0}^{\infty}\prod_{k=1}^{n}(kx-1)e^{-ax} {d}x,$ where $a$ and $n$ are parameters.

Limit involving Gamma function

Integral in terms of gamma

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