Question

Is there $b$ depending only on $a$ such that $\prod_{i=1}^n \Gamma(\lambda_i a) \le b$ for all $\lambda_i >0$ s.t. $\sum \lambda_i = 1$?

score 20 · Answer 1 · 2026-04-03 00:50:33

Is there $b$ depending only on $a$ such that $\prod_{i=1}^n \Gamma(\lambda_i a) \le b$ for all $\lambda_i >0$ s.t. $\sum \lambda_i = 1$?

score 159 · Answer 2 · 2026-04-10 23:34:22

159

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Monotonicity of a ratio of Gamma functions

Published on 10 Apr 2026 - 23:34

score 248 · Answer 3 · 2026-03-30 06:14:41

248

Views

Show the inequality $\frac{\sqrt{\pi}}{2}<\left(\pi-e\right)!$

Published on 30 Mar 2026 - 6:14

score 117 · Answer 4 · 2026-03-28 16:13:35

117

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The integral $\int_{0}^{\pi/2} \tan^p x~dx$

Published on 28 Mar 2026 - 16:13

score 159 · Answer 5 · 2026-03-26 07:30:57

159

Views

Prove $(n-1)! + 1 = n^2$ has only one integer solution

Published on 26 Mar 2026 - 7:30

score 60 · Answer 6 · 2026-04-13 04:39:15

60

Views

Definite Integral of $\text{exp}(-(\sum_i |x_i|^a)^b)$

Published on 13 Apr 2026 - 4:39

score 68 · Answer 7 · 2026-03-30 16:09:54

68

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Looking for $B$ such that $\Gamma(ax+b) \prod_{i=1}^n (ax+e_i)\sim \Gamma(ax+B)$

Published on 30 Mar 2026 - 16:09

score 123 · Answer 8 · 2022-06-02 22:49:05

123

Views

Neat function $I(x,y)= \sum\limits_{n=1}^{\infty}\bigg|\int_0^1 \frac{1}{t~(\log t)^y}\exp\bigg(\frac{n^x}{\log t}\bigg) ~dt~\bigg| $. Closed form?

Published on 02 Jun 2022 - 22:49

score 17 · Answer 9 · 2026-03-11 19:49:01

17

Views

How do software packages compute the gamma probability density for large $\alpha$?

Published on 11 Mar 2026 - 19:49

score 90 · Answer 10 · 2022-06-05 05:16:31

90

Views

Let $a>0$. Prove the improper integral $\int_0^{\infty} \cos\left\{{a\over2}\left(x+{1\over x}\right)\right\}x^{k-2}\ dx$ converges for $k>2$

Published on 05 Jun 2022 - 5:16

score 196 · Answer 11 · 2026-04-12 20:34:49

196

Views

Minimum of the Gamma function

Published on 12 Apr 2026 - 20:34

score 114 · Answer 12 · 2022-06-08 01:18:21

114

Views

Lower bound on the upper incomplete Gamma function

Published on 08 Jun 2022 - 1:18

score 96 · Answer 13 · 2026-04-13 09:58:08

96

Views

Complex Parts of the Gamma function

Published on 13 Apr 2026 - 9:58

score 122 · Answer 14 · 2022-06-10 08:23:52

122

Views

$-2(-1)^n\zeta(n)=\lim_{m\to\infty}m^n\left(\displaystyle\prod_{k=1}^n\Gamma\left(1+\frac{\zeta_n^k}{m}\right)^{-2}-1\right).$

Published on 10 Jun 2022 - 8:23

score 145 · Answer 15 · 2026-04-13 08:54:15

145

Views

How to solve such complicated integration involving product of two lower incomplete Gamma function?

Published on 13 Apr 2026 - 8:54

List Question

Is there $b$ depending only on $a$ such that $\prod_{i=1}^n \Gamma(\lambda_i a) \le b$ for all $\lambda_i >0$ s.t. $\sum \lambda_i = 1$?

Monotonicity of a ratio of Gamma functions

Show the inequality $\frac{\sqrt{\pi}}{2}<\left(\pi-e\right)!$

The integral $\int_{0}^{\pi/2} \tan^p x~dx$

Prove $(n-1)! + 1 = n^2$ has only one integer solution

Definite Integral of $\text{exp}(-(\sum_i |x_i|^a)^b)$

Looking for $B$ such that $\Gamma(ax+b) \prod_{i=1}^n (ax+e_i)\sim \Gamma(ax+B)$

Neat function $I(x,y)= \sum\limits_{n=1}^{\infty}\bigg|\int_0^1 \frac{1}{t~(\log t)^y}\exp\bigg(\frac{n^x}{\log t}\bigg) ~dt~\bigg| $. Closed form?

How do software packages compute the gamma probability density for large $\alpha$?

Let $a>0$. Prove the improper integral $\int_0^{\infty} \cos\left\{{a\over2}\left(x+{1\over x}\right)\right\}x^{k-2}\ dx$ converges for $k>2$

Minimum of the Gamma function

Lower bound on the upper incomplete Gamma function

Complex Parts of the Gamma function

$-2(-1)^n\zeta(n)=\lim_{m\to\infty}m^n\left(\displaystyle\prod_{k=1}^n\Gamma\left(1+\frac{\zeta_n^k}{m}\right)^{-2}-1\right).$

How to solve such complicated integration involving product of two lower incomplete Gamma function?

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