Question

Closed from for the series involving gamma function

score 138 · Answer 1 · 2021-09-06 15:30:24

138

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Closed from for the series involving gamma function

Published on 06 Sep 2021 - 15:30

score 56 · Answer 2 · 2026-04-08 22:49:04

56

Views

Proof of equality involving logged fraction of Gamma functions

Published on 08 Apr 2026 - 22:49

score 189 · Answer 3 · 2026-03-28 09:28:39

189

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A series expansion for $\left(x^2\,B(x,x)\right)^\frac nx$ or $\frac{1}{(Γ(2x))^\frac nx}$ for $0\lt x\le 1, n\in\Bbb N$

Published on 28 Mar 2026 - 9:28

score 53 · Answer 4 · 2026-04-08 17:32:40

53

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Existence/value of the integral of a rational function using gamma function and complex analysis

Published on 08 Apr 2026 - 17:32

score 48 · Answer 5 · 2026-04-11 22:31:49

48

Views

Ask for a proof of an inequality bounding the ratio of two consecutive geometric means of the first finitely many natural numbers

Published on 11 Apr 2026 - 22:31

score 100 · Answer 6 · 2026-03-26 06:20:36

100

Views

Difference between finding asymptotics of Beta function through Laplace versus through Stirling

Published on 26 Mar 2026 - 6:20

score 65 · Answer 7 · 2026-04-12 06:13:35

65

Views

Expected value of a continous generalization of the negative binomial distribution

Published on 12 Apr 2026 - 6:13

score 98 · Answer 8 · 2026-04-06 21:15:48

98

Views

How to show that $(ex)^{-1}\leq \Gamma (x) \leq 1+1/x$, if $0<x<1$?

Published on 06 Apr 2026 - 21:15

score 143 · Answer 9 · 2021-09-18 06:50:40

143

Views

Prove that $ \int_0^1\frac{x\ln(x)}{1+x^2+x^4}dx=\frac{1}{36}\Big(\psi^{(1)}(2/3)-\psi^{(1)}(1/3)\Big) $

Published on 18 Sep 2021 - 6:50

score 87 · Answer 10 · 2026-04-12 15:00:30

87

Views

The sum $\sum_{i=1}^\infty \frac{1}{i!i}$

Published on 12 Apr 2026 - 15:00

score 513 · Answer 11 · 2026-03-29 17:25:26

513

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How to evaluate $\sum\limits_{x=0}^\infty \text{erfc}(x)= 1.1619990479471263635323…?$

Published on 29 Mar 2026 - 17:25

score 118 · Answer 12 · 2026-04-06 22:45:43

118

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A lower bound for the Gamma function : $\Gamma(x)\geq (f(1-x))^x$ on $1\leq x \leq 2$

Published on 06 Apr 2026 - 22:45

score 296 · Answer 13 · 2026-04-12 06:53:15

296

Views

What is the positive solution to $\Gamma'(x)=0$?

Published on 12 Apr 2026 - 6:53

score 73 · Answer 14 · 2021-09-22 23:05:43

73

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Show that $2 t f^{\prime}(t)-(2 t+1) f(t)+\frac{1}{\sqrt{\pi}}=0$

Published on 22 Sep 2021 - 23:05

score 48 · Answer 15 · 2021-09-23 11:49:00

48

Views

Proof the inequality of Gamma function $\Gamma\left(\frac{1}{2}+it \right)\geq N! \,\bigg|\Gamma\left(-N-\frac{1}{2}+it \right)\bigg|$

Published on 23 Sep 2021 - 11:49

List Question

Closed from for the series involving gamma function

Proof of equality involving logged fraction of Gamma functions

A series expansion for $\left(x^2\,B(x,x)\right)^\frac nx$ or $\frac{1}{(Γ(2x))^\frac nx}$ for $0\lt x\le 1, n\in\Bbb N$

Existence/value of the integral of a rational function using gamma function and complex analysis

Ask for a proof of an inequality bounding the ratio of two consecutive geometric means of the first finitely many natural numbers

Difference between finding asymptotics of Beta function through Laplace versus through Stirling

Expected value of a continous generalization of the negative binomial distribution

How to show that $(ex)^{-1}\leq \Gamma (x) \leq 1+1/x$, if $0<x<1$?

Prove that $ \int_0^1\frac{x\ln(x)}{1+x^2+x^4}dx=\frac{1}{36}\Big(\psi^{(1)}(2/3)-\psi^{(1)}(1/3)\Big) $

The sum $\sum_{i=1}^\infty \frac{1}{i!i}$

How to evaluate $\sum\limits_{x=0}^\infty \text{erfc}(x)= 1.1619990479471263635323…?$

A lower bound for the Gamma function : $\Gamma(x)\geq (f(1-x))^x$ on $1\leq x \leq 2$

What is the positive solution to $\Gamma'(x)=0$?

Show that $2 t f^{\prime}(t)-(2 t+1) f(t)+\frac{1}{\sqrt{\pi}}=0$

Proof the inequality of Gamma function $\Gamma\left(\frac{1}{2}+it \right)\geq N! \,\bigg|\Gamma\left(-N-\frac{1}{2}+it \right)\bigg|$

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