List questions from gamma-function

Published on 13 Nov 2020 - 18:43

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Prove the inequality $\ln\left(\Gamma(x^x+1)\right)< x^x\ln\left(\Gamma(x+1)\right)$ for $0<x<1$

Published on 15 Nov 2020 - 17:58

74

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Show that $\Gamma\left(3^{-3}+1\right)<\Gamma \left(\operatorname{W}(3)^{-\operatorname{W}(3)}+1\right)$

Published on 28 Mar 2026 - 10:24

208

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Integral using Gamma and Beta function

Published on 28 Mar 2026 - 2:41

99

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Expressing the solution of integral using Special functions Gamma or/and Beta functions?

Published on 28 Mar 2026 - 2:49

69

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Contour integral of fraction (involving Gamma function) = Polynomial

Published on 07 Apr 2026 - 21:12

121

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How I prove absolute convergence of this infinite product?

Published on 25 Mar 2026 - 9:27

694

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Proving euler's reflection formula

Published on 28 Mar 2026 - 2:41

75

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Integral over bounded $V$: $\idotsint _V\prod_{i=1}^{n}x_i^{a_i-1}d^nx$

Published on 02 Apr 2026 - 14:18

133

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Naive way to calculate the minimum of the Gamma function .

Published on 21 Nov 2020 - 13:36

51

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Show $\Gamma(z)y^{-z}$ vanishes as $z\to\pm i\infty$

Published on 22 Nov 2020 - 9:55

240

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How to simplify out of the gamma function $\Gamma(z)$?

Published on 23 Feb 2026 - 15:50

173

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Convergence of $\int_{x=0}^\infty x^8 e^{-\sqrt x} dx$

Published on 24 Nov 2020 - 23:59

65

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Why does $\frac{d}{d\nu}\ln\Gamma\left(\frac{\nu}{2}\right)$ simplify to digamma function?

Published on 26 Mar 2026 - 1:03

686

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Mellin transformation of $\cos(z)$ and $\sin(z)$ [Stein Complex Chapter 6 Exercise 10(a)]

Published on 26 Nov 2020 - 22:23

List Question

Proving the duplication formula

Prove the inequality $\ln\left(\Gamma(x^x+1)\right)< x^x\ln\left(\Gamma(x+1)\right)$ for $0<x<1$

Show that $\Gamma\left(3^{-3}+1\right)<\Gamma \left(\operatorname{W}(3)^{-\operatorname{W}(3)}+1\right)$

Integral using Gamma and Beta function

Expressing the solution of integral using Special functions Gamma or/and Beta functions?

Contour integral of fraction (involving Gamma function) = Polynomial

How I prove absolute convergence of this infinite product?

Proving euler's reflection formula

Integral over bounded $V$: $\idotsint _V\prod_{i=1}^{n}x_i^{a_i-1}d^nx$

Naive way to calculate the minimum of the Gamma function .

Show $\Gamma(z)y^{-z}$ vanishes as $z\to\pm i\infty$

How to simplify out of the gamma function $\Gamma(z)$?

Convergence of $\int_{x=0}^\infty x^8 e^{-\sqrt x} dx$

Why does $\frac{d}{d\nu}\ln\Gamma\left(\frac{\nu}{2}\right)$ simplify to digamma function?

Mellin transformation of $\cos(z)$ and $\sin(z)$ [Stein Complex Chapter 6 Exercise 10(a)]

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