Question

Expand ratio of gamma functions into series

score 52 · Answer 1 · 2019-06-22 02:48:48

52

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Expand ratio of gamma functions into series

Published on 22 Jun 2019 - 2:48

score 142 · Answer 2 · 2019-06-25 19:39:19

142

Views

How to integrate $\int_0^{\infty} \frac{\sin(x^{-p})}{x^2}dx$ where $p>1$?

Published on 25 Jun 2019 - 19:39

score 127 · Answer 3 · 2019-06-28 07:46:25

127

Views

integral involves incomplete gamma function and $x^{-1}$

Published on 28 Jun 2019 - 7:46

score 193 · Answer 4 · 2026-03-27 03:44:14

193

Views

Prove $\sum_{n=1}^{\infty}\frac{\Gamma(n+\frac{1}{2})}{(2n+1)(2n+2)(n-1)!}=\frac{(4-π)\sqrt{\pi}}{4}$

Published on 27 Mar 2026 - 3:44

score 183 · Answer 5 · 2019-06-29 15:40:02

Prove the following identity of Gamma : $\frac{\Gamma(\frac{7}{8})}{\Gamma(\frac{3}{8})}=\frac{(1+\sqrt{2})\Gamma(\frac{5}{8})}{\Gamma(\frac{1}{8})}$

score 39 · Answer 6 · 2019-06-30 11:56:17

39

Views

Dose exist closed form for $ I=\int_{x=0}^{\alpha}x^{n-1}e^{-x\beta}\gamma(m,(\alpha-x)\zeta) $

Published on 30 Jun 2019 - 11:56

score 70 · Answer 7 · 2026-03-25 03:07:26

70

Views

Simplifcation of an summation of gamma functions by Mathematica

Published on 25 Mar 2026 - 3:07

score 199 · Answer 8 · 2019-07-03 02:06:51

199

Views

The Puiseux series and gamma function

Published on 03 Jul 2019 - 2:06

score 139 · Answer 9 · 2026-03-25 11:10:04

139

Views

Complex integral related to incomplete gamma function

Published on 25 Mar 2026 - 11:10

score 132 · Answer 10 · 2019-07-03 07:21:31

132

Views

Series involving gamma function

Published on 03 Jul 2019 - 7:21

score 31 · Answer 11 · 2019-07-06 19:38:38

31

Views

Product of the incomplete gamma function and a monomial

Published on 06 Jul 2019 - 19:38

score 304 · Answer 12 · 2019-07-07 09:19:31

Prove that $\int_{0}^{\infty} \int_{0}^{1} \frac{\sin (\pi x)}{\pi} e^{-t} t^{-x} d t d x=e+\int_{0}^{1} \frac{e^{-t}}{\pi^{2}+\log ^{2}(t)} d t$

score 1.1k · Answer 13 · 2019-07-07 10:52:09

1.1k

Views

Help in proving, that $\int_{0}^{\infty} \frac{1}{\Gamma(x)} d x=e+\int_{0}^{\infty} \frac{e^{-x}}{\pi^{2}+(\ln x)^{2}} d x$ using real methods only

Published on 07 Jul 2019 - 10:52

score 216 · Answer 14 · 2026-03-26 06:28:30

216

Views

How can Weierstrass product for the gamma function reduce to Wallis formula for $\pi$?

Published on 26 Mar 2026 - 6:28

score 118 · Answer 15 · 2026-03-25 13:33:28

118

Views

Fransén-Robinson Constant and an intriguing series

Published on 25 Mar 2026 - 13:33

List Question

Expand ratio of gamma functions into series

How to integrate $\int_0^{\infty} \frac{\sin(x^{-p})}{x^2}dx$ where $p>1$?

integral involves incomplete gamma function and $x^{-1}$

Prove $\sum_{n=1}^{\infty}\frac{\Gamma(n+\frac{1}{2})}{(2n+1)(2n+2)(n-1)!}=\frac{(4-π)\sqrt{\pi}}{4}$

Prove the following identity of Gamma : $\frac{\Gamma(\frac{7}{8})}{\Gamma(\frac{3}{8})}=\frac{(1+\sqrt{2})\Gamma(\frac{5}{8})}{\Gamma(\frac{1}{8})}$

Dose exist closed form for $ I=\int_{x=0}^{\alpha}x^{n-1}e^{-x\beta}\gamma(m,(\alpha-x)\zeta) $

Simplifcation of an summation of gamma functions by Mathematica

The Puiseux series and gamma function

Complex integral related to incomplete gamma function

Series involving gamma function

Product of the incomplete gamma function and a monomial

Prove that $\int_{0}^{\infty} \int_{0}^{1} \frac{\sin (\pi x)}{\pi} e^{-t} t^{-x} d t d x=e+\int_{0}^{1} \frac{e^{-t}}{\pi^{2}+\log ^{2}(t)} d t$

Help in proving, that $\int_{0}^{\infty} \frac{1}{\Gamma(x)} d x=e+\int_{0}^{\infty} \frac{e^{-x}}{\pi^{2}+(\ln x)^{2}} d x$ using real methods only

How can Weierstrass product for the gamma function reduce to Wallis formula for $\pi$?

Fransén-Robinson Constant and an intriguing series

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