Question

A calculation about the sum of the product of Binomial and Stirling numbers of the first kind

score 90 · Answer 1 · 2026-04-11 18:47:25

90

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A calculation about the sum of the product of Binomial and Stirling numbers of the first kind

Published on 11 Apr 2026 - 18:47

score 156 · Answer 2 · 2021-10-22 19:02:25

156

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Proving $\lim_{x\to\infty}\frac{\Gamma(x)}{\Gamma(x+\varepsilon)}=0$ for all $\varepsilon>0$.

Published on 22 Oct 2021 - 19:02

score 295 · Answer 3 · 2026-04-11 20:56:22

295

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Context, name or explanation for a formula in the "law of rare events"

Published on 11 Apr 2026 - 20:56

score 291 · Answer 4 · 2026-04-12 23:13:46

291

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How might one make this Gaussian integral derivation of Stirling's approximation more airtight?

Published on 12 Apr 2026 - 23:13

score 77 · Answer 5 · 2021-10-28 09:54:14

77

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$\sum_{k=0}^{\infty}\frac{ (-1)^{k} \Gamma(\frac{2k+n+m}{2})\Gamma(\frac{2k+m-1}{2})}{2^{2k}k!\Gamma(k+\frac{m}{2})} z^{2k}$ is an elementary function

Published on 28 Oct 2021 - 9:54

score 138 · Answer 6 · 2021-10-28 13:05:56

138

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Compute $\int\limits_0^{\infty}\frac{(v - \lambda)^2}\lambda\exp(\frac {\text -v}{\lambda}) \,\mathrm dv$

Published on 28 Oct 2021 - 13:05

score 76 · Answer 7 · 2021-10-29 02:22:28

Proving $\int_0^\infty \frac{1-\cos(at)}{t^{1+\alpha}} \mathrm dt =\frac{\pi}{2 \Gamma(\alpha+1) \sin(\alpha \pi /2)} |a|^\alpha $

score 758 · Answer 8 · 2021-10-29 14:33:17

758

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Evaluate $\int_{0}^{\infty}2^{-ax^2}dx$ by using Gamma function

Published on 29 Oct 2021 - 14:33

score 460 · Answer 9 · 2026-03-28 09:33:34

460

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How to evaluate the integral $I = \int_o^{\infty} \frac{x}{\sqrt{e^{2\pi\sqrt{x}}-1}}dx$?

Published on 28 Mar 2026 - 9:33

score 322 · Answer 10 · 2026-04-10 02:35:41

322

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Mittag-Leffler Expansion of gamma function

Published on 10 Apr 2026 - 2:35

score 97 · Answer 11 · 2026-04-09 09:20:52

97

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Question on properties of Gamma functions

Published on 09 Apr 2026 - 9:20

score 66 · Answer 12 · 2026-03-30 16:56:50

66

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How to compute $I_{m,n,k}=\int_{0}^{\infty} \frac{dx}{\sinh^n(x) \coth^{2k+n+m-1}(x)}$?

Published on 30 Mar 2026 - 16:56

score 336 · Answer 13 · 2021-11-02 22:13:25

336

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$\sum_{k=0}^{\infty} \Gamma\left(k+\alpha\right) \, \frac{t^k}{k!}=??$

Published on 02 Nov 2021 - 22:13

score 289 · Answer 14 · 2026-03-26 06:08:12

289

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$\frac {\zeta(2)}{e^2} + \frac {\zeta(3)}{e^3} + \frac {\zeta(4)}{e^4} + \frac {\zeta(5)}{e^5}.....?$

Published on 26 Mar 2026 - 6:08

score 52 · Answer 15 · 2026-04-11 03:17:07

52

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Gamma function as the ratio of two holomorphic functions

Published on 11 Apr 2026 - 3:17

List Question

A calculation about the sum of the product of Binomial and Stirling numbers of the first kind

Proving $\lim_{x\to\infty}\frac{\Gamma(x)}{\Gamma(x+\varepsilon)}=0$ for all $\varepsilon>0$.

Context, name or explanation for a formula in the "law of rare events"

How might one make this Gaussian integral derivation of Stirling's approximation more airtight?

$\sum_{k=0}^{\infty}\frac{ (-1)^{k} \Gamma(\frac{2k+n+m}{2})\Gamma(\frac{2k+m-1}{2})}{2^{2k}k!\Gamma(k+\frac{m}{2})} z^{2k}$ is an elementary function

Compute $\int\limits_0^{\infty}\frac{(v - \lambda)^2}\lambda\exp(\frac {\text -v}{\lambda}) \,\mathrm dv$

Proving $\int_0^\infty \frac{1-\cos(at)}{t^{1+\alpha}} \mathrm dt =\frac{\pi}{2 \Gamma(\alpha+1) \sin(\alpha \pi /2)} |a|^\alpha $

Evaluate $\int_{0}^{\infty}2^{-ax^2}dx$ by using Gamma function

How to evaluate the integral $I = \int_o^{\infty} \frac{x}{\sqrt{e^{2\pi\sqrt{x}}-1}}dx$?

Mittag-Leffler Expansion of gamma function

Question on properties of Gamma functions

How to compute $I_{m,n,k}=\int_{0}^{\infty} \frac{dx}{\sinh^n(x) \coth^{2k+n+m-1}(x)}$?

$\sum_{k=0}^{\infty} \Gamma\left(k+\alpha\right) \, \frac{t^k}{k!}=??$

$\frac {\zeta(2)}{e^2} + \frac {\zeta(3)}{e^3} + \frac {\zeta(4)}{e^4} + \frac {\zeta(5)}{e^5}.....?$

Gamma function as the ratio of two holomorphic functions

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