Question

Distribution-like integral

score 44 · Answer 1 · 2017-12-21 03:22:21

44

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Distribution-like integral

Published on 21 Dec 2017 - 3:22

score 50 · Answer 2 · 2017-12-22 18:25:53

50

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Show that $\frac{\Gamma(1 + x)}{\Gamma(1 + x + n)} \leq \frac{1}{\Gamma(n+1)}$ for $x \in (0,1), n \in \mathbb{N}$

Published on 22 Dec 2017 - 18:25

score 96 · Answer 3 · 2017-12-22 18:45:44

96

Views

How could I approach a limit question of the Barnes G-function?

Published on 22 Dec 2017 - 18:45

score 585 · Answer 4 · 2017-12-23 12:10:53

585

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Gamma Function derivation using differentiation of definite integral?

Published on 23 Dec 2017 - 12:10

score 1.7k · Answer 5 · 2026-03-26 19:23:46

1.7k

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Gamma kernel Density estimator

Published on 26 Mar 2026 - 19:23

score 173 · Answer 6 · 2017-12-30 17:08:52

173

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Evaluate $\int_0^{\pi/2}\frac{1-\sqrt[18]{\cos u}}{1-\cos u}du$, in terms of particular values of special functions and constants

Published on 30 Dec 2017 - 17:08

score 137 · Answer 7 · 2026-03-30 20:31:29

137

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Partial Fraction Decomposition of $\prod\limits_{j=0}^{n}\frac 1{1+Xa^{j-k}}$

Published on 30 Mar 2026 - 20:31

score 326 · Answer 8 · 2018-01-02 20:57:44

326

Views

Can we prove this factorial interpolation process converges to the Gamma function?

Published on 02 Jan 2018 - 20:57

score 238 · Answer 9 · 2026-03-28 05:22:07

238

Views

Yet another request for how to do the Inverse (Gamma(x-1) Function -- involves Lambert W

Published on 28 Mar 2026 - 5:22

score 59 · Answer 10 · 2018-01-07 15:47:47

59

Views

Variations and limits of $x \mapsto \int_0^1 e^{-t} t^{x - 1} \textrm{d}t$

Published on 07 Jan 2018 - 15:47

score 52 · Answer 11 · 2018-01-08 21:41:10

52

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Justify if it is possible to interchange the integral sign and the series: a series involving the Möbius function and loggamma terms

Published on 08 Jan 2018 - 21:41

score 91 · Answer 12 · 2018-01-09 02:56:45

91

Views

How to integrate the following gamma type function

Published on 09 Jan 2018 - 2:56

score 44 · Answer 13 · 2018-01-10 23:08:28

44

Views

Calculating $\Gamma'(n)$ for $n \in \mathbb{N}^{*}$

Published on 10 Jan 2018 - 23:08

score 425 · Answer 14 · 2018-01-12 11:32:38

425

Views

$\int_0^1\int_0^1\binom{\text{something}}{\text{something}}\binom{\text{something}}{\text{something}}\cdot \text{something }dxdy$ with closed-form

Published on 12 Jan 2018 - 11:32

score 19.3k · Answer 15 · 2026-04-07 05:42:58

19.3k

Views

Why is Euler's Gamma function the "best" extension of the factorial function to the reals?

Published on 07 Apr 2026 - 5:42

List Question

Distribution-like integral

Show that $\frac{\Gamma(1 + x)}{\Gamma(1 + x + n)} \leq \frac{1}{\Gamma(n+1)}$ for $x \in (0,1), n \in \mathbb{N}$

How could I approach a limit question of the Barnes G-function?

Gamma Function derivation using differentiation of definite integral?

Gamma kernel Density estimator

Evaluate $\int_0^{\pi/2}\frac{1-\sqrt[18]{\cos u}}{1-\cos u}du$, in terms of particular values of special functions and constants

Partial Fraction Decomposition of $\prod\limits_{j=0}^{n}\frac 1{1+Xa^{j-k}}$

Can we prove this factorial interpolation process converges to the Gamma function?

Yet another request for how to do the Inverse (Gamma(x-1) Function -- involves Lambert W

Variations and limits of $x \mapsto \int_0^1 e^{-t} t^{x - 1} \textrm{d}t$

Justify if it is possible to interchange the integral sign and the series: a series involving the Möbius function and loggamma terms

How to integrate the following gamma type function

Calculating $\Gamma'(n)$ for $n \in \mathbb{N}^{*}$

$\int_0^1\int_0^1\binom{\text{something}}{\text{something}}\binom{\text{something}}{\text{something}}\cdot \text{something }dxdy$ with closed-form

Why is Euler's Gamma function the "best" extension of the factorial function to the reals?

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