Question

Find reference about expansion of gamma function

score 31 · Answer 1 · 2026-04-11 08:38:24

31

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Find reference about expansion of gamma function

Published on 11 Apr 2026 - 8:38

score 89 · Answer 2 · 2026-04-14 01:41:26

89

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What is the value of this Gamma type integral?

Published on 14 Apr 2026 - 1:41

score 51 · Answer 3 · 2026-04-13 06:39:42

51

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What is the value of this integral whose integrand is a mixture of gamma and gaussian functions?

Published on 13 Apr 2026 - 6:39

score 101 · Answer 4 · 2026-04-13 11:44:05

101

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$\int_0^\infty 3^{-x^2} dx$ using gamma function

Published on 13 Apr 2026 - 11:44

score 53 · Answer 5 · 2022-11-02 12:37:47

53

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Does we have $\int_{\sum_{i=1}^{\frac{p}{k}}\frac{1}{i}}^{\sum_{i=1}^{p}\frac{1}{i}}e^{-\left(\frac{x}{p}\right)^{p}}dx\to \ln(k)$ as $p\to \infty$?

Published on 02 Nov 2022 - 12:37

score 121 · Answer 6 · 2022-11-03 13:31:22

121

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Show by hand $\int_{0}^{1}\cot\left(e^{-x^{2}}\right)!dx<\int_{0}^{1}x^{-x}dx$

Published on 03 Nov 2022 - 13:31

score 105 · Answer 7 · 2026-04-10 02:21:08

105

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Upperbound for an integral

Published on 10 Apr 2026 - 2:21

score 96 · Answer 8 · 2026-04-10 02:10:14

96

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Stein complex analysis 6.2

Published on 10 Apr 2026 - 2:10

score 33 · Answer 9 · 2022-11-15 03:37:26

Show $\lim_{n\to\infty}\frac{\sum_{k=1}^{n}(\frac{\Gamma(k-c\lambda)}{\Gamma(k+a\lambda)})^{2}}{n^{1-2(a+c)\lambda}}=\frac{1}{1-2(a+c)\lambda}$

score 55 · Answer 10 · 2026-04-14 01:33:57

55

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Chainging the hypergeometric series $F(\alpha,\beta,\gamma;z)$ to an integral form

Published on 14 Apr 2026 - 1:33

score 195 · Answer 11 · 2026-03-28 05:23:09

195

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Show that the identity $\int_0^\infty\sin(t)t^{z-1}\ dt = \Gamma(z)\sin\left(\pi{z\over 2}\right)$ holds on $-1<\operatorname{Re}(z)<1$

Published on 28 Mar 2026 - 5:23

score 37 · Answer 12 · 2026-04-09 05:57:40

37

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How to find the divergent behavior for a function with $Gamma$ function

Published on 09 Apr 2026 - 5:57

score 62 · Answer 13 · 2026-03-27 09:13:51

62

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How to do the integral $\int \frac{d^{D}k}{(2\pi)^{D}} \frac{1-\cos(\vec{k}\cdot \vec{x})}{k^2}$?

Published on 27 Mar 2026 - 9:13

score 85 · Answer 14 · 2022-11-19 14:25:23

85

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Contour integrals on the complex plane: $\int_{\mathcal{C}_\rho^+} z^\delta e^{i z x} \mathrm{d} z$ on the top half-circle.

Published on 19 Nov 2022 - 14:25

score 66 · Answer 15 · 2026-04-13 12:25:27

66

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Relation between beta and gamma function by an elementary method :

Published on 13 Apr 2026 - 12:25

List Question

Find reference about expansion of gamma function

What is the value of this Gamma type integral?

What is the value of this integral whose integrand is a mixture of gamma and gaussian functions?

$\int_0^\infty 3^{-x^2} dx$ using gamma function

Does we have $\int_{\sum_{i=1}^{\frac{p}{k}}\frac{1}{i}}^{\sum_{i=1}^{p}\frac{1}{i}}e^{-\left(\frac{x}{p}\right)^{p}}dx\to \ln(k)$ as $p\to \infty$?

Show by hand $\int_{0}^{1}\cot\left(e^{-x^{2}}\right)!dx<\int_{0}^{1}x^{-x}dx$

Upperbound for an integral

Stein complex analysis 6.2

Show $\lim_{n\to\infty}\frac{\sum_{k=1}^{n}(\frac{\Gamma(k-c\lambda)}{\Gamma(k+a\lambda)})^{2}}{n^{1-2(a+c)\lambda}}=\frac{1}{1-2(a+c)\lambda}$

Chainging the hypergeometric series $F(\alpha,\beta,\gamma;z)$ to an integral form

Show that the identity $\int_0^\infty\sin(t)t^{z-1}\ dt = \Gamma(z)\sin\left(\pi{z\over 2}\right)$ holds on $-1<\operatorname{Re}(z)<1$

How to find the divergent behavior for a function with $Gamma$ function

How to do the integral $\int \frac{d^{D}k}{(2\pi)^{D}} \frac{1-\cos(\vec{k}\cdot \vec{x})}{k^2}$?

Contour integrals on the complex plane: $\int_{\mathcal{C}_\rho^+} z^\delta e^{i z x} \mathrm{d} z$ on the top half-circle.

Relation between beta and gamma function by an elementary method :

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