Question

On the integral $\frac{1}{2\pi i}\int_{c-iT}^{c+iT}\frac{\Gamma\left(w\right)}{\Gamma\left(w+\alpha\right)}dw$

score 170 · Answer 1 · 2026-03-26 00:53:47

170

Views

On the integral $\frac{1}{2\pi i}\int_{c-iT}^{c+iT}\frac{\Gamma\left(w\right)}{\Gamma\left(w+\alpha\right)}dw$

Published on 26 Mar 2026 - 0:53

score 206 · Answer 2 · 2017-09-17 01:12:20

206

Views

Gamma function manipulation $\Gamma\left(x+\frac{1}{2}\right) = \text{something}\Gamma(x)$?

Published on 17 Sep 2017 - 1:12

score 145 · Answer 3 · 2026-04-04 00:35:34

145

Views

Assymptotics of incomplete gamma function $\gamma(x /\ln 2,x)$

Published on 04 Apr 2026 - 0:35

score 112 · Answer 4 · 2017-09-19 09:42:48

112

Views

To test the convergence of $\int _0^1 \frac{\ln x}{(x^2 +1)}\, \mathrm dx $

Published on 19 Sep 2017 - 9:42

score 62 · Answer 5 · 2017-09-19 16:03:48

62

Views

Proving $\int_{0}^{\infty} u^{x-1}e^{-u} du = 2 \int_{0}^{\infty} u^{2x-1}e^{-u^2} du$

Published on 19 Sep 2017 - 16:03

score 262 · Answer 6 · 2026-03-26 17:36:03

262

Views

Behavior of Gamma Distribution over time

Published on 26 Mar 2026 - 17:36

score 311 · Answer 7 · 2026-03-26 09:49:35

311

Views

Solving finite sum in terms of the generalized hypergeometric function

Published on 26 Mar 2026 - 9:49

score 310 · Answer 8 · 2017-09-22 00:14:15

310

Views

Lower bound on a ratio of factorials

Published on 22 Sep 2017 - 0:14

score 63 · Answer 9 · 2017-09-27 02:39:11

63

Views

Dose $\sum_n^{\infty}\frac{z^n}{(\Gamma(z-n+1)n!}$ converge for any values of z other then $0$

Published on 27 Sep 2017 - 2:39

score 335 · Answer 10 · 2026-03-27 23:23:36

335

Views

Closed form solution for $\int_{0}^{2\pi}|\cos^N x||\sin^M x|\cos^n x\sin^m x dx$

Published on 27 Mar 2026 - 23:23

score 248 · Answer 11 · 2026-03-28 06:40:48

248

Views

Series related to the (lower) incomplete gamma function $\gamma(a,x)$ with $x<0$

Published on 28 Mar 2026 - 6:40

score 35 · Answer 12 · 2026-04-04 13:14:10

35

Views

For $1\leq x<2$, $\frac{n^{-x}}{n!}x(x+1)\cdots(x+n)$ is lower bounded

Published on 04 Apr 2026 - 13:14

score 757 · Answer 13 · 2026-03-27 23:21:46

757

Views

Beta Gamma functions

Published on 27 Mar 2026 - 23:21

score 46 · Answer 14 · 2026-03-25 19:04:01

46

Views

Computing $\lim_{\varepsilon\to 0^{+}}\psi(\varepsilon)/\Gamma(\varepsilon)$ with asymptotic expansions

Published on 25 Mar 2026 - 19:04

score 52 · Answer 15 · 2017-10-05 06:42:38

52

Views

There is a $p\in(0,1)$ such that $\lim_{n\to\infty}\binom{2n}n p^n\in (0,\infty)$?

Published on 05 Oct 2017 - 6:42

List Question

On the integral $\frac{1}{2\pi i}\int_{c-iT}^{c+iT}\frac{\Gamma\left(w\right)}{\Gamma\left(w+\alpha\right)}dw$

Gamma function manipulation $\Gamma\left(x+\frac{1}{2}\right) = \text{something}\Gamma(x)$?

Assymptotics of incomplete gamma function $\gamma(x /\ln 2,x)$

To test the convergence of $\int _0^1 \frac{\ln x}{(x^2 +1)}\, \mathrm dx $

Proving $\int_{0}^{\infty} u^{x-1}e^{-u} du = 2 \int_{0}^{\infty} u^{2x-1}e^{-u^2} du$

Behavior of Gamma Distribution over time

Solving finite sum in terms of the generalized hypergeometric function

Lower bound on a ratio of factorials

Dose $\sum_n^{\infty}\frac{z^n}{(\Gamma(z-n+1)n!}$ converge for any values of z other then $0$

Closed form solution for $\int_{0}^{2\pi}|\cos^N x||\sin^M x|\cos^n x\sin^m x dx$

Series related to the (lower) incomplete gamma function $\gamma(a,x)$ with $x<0$

For $1\leq x<2$, $\frac{n^{-x}}{n!}x(x+1)\cdots(x+n)$ is lower bounded

Beta Gamma functions

Computing $\lim_{\varepsilon\to 0^{+}}\psi(\varepsilon)/\Gamma(\varepsilon)$ with asymptotic expansions

There is a $p\in(0,1)$ such that $\lim_{n\to\infty}\binom{2n}n p^n\in (0,\infty)$?

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