Question

Show that $\frac{\Gamma(n+k)}{\Gamma(n)}\sim n^k$ for large values of n

score 317 · Answer 1 · 2016-03-28 12:58:43

317

Views

Show that $\frac{\Gamma(n+k)}{\Gamma(n)}\sim n^k$ for large values of n

Published on 28 Mar 2016 - 12:58

score 189 · Answer 2 · 2026-04-04 07:37:26

189

Views

Evaluating the integral $\int_{-\infty}^{\infty} \frac{(1-ix)^{n-s_1}}{(1+ix)^{n+s_2}} dx$.

Published on 04 Apr 2026 - 7:37

score 71 · Answer 3 · 2016-04-01 02:58:39

71

Views

Sum of Gamma functions (product pairs)

Published on 01 Apr 2016 - 2:58

score 127 · Answer 4 · 2016-04-02 15:10:50

127

Views

How to calculate $\int_{0}^{\infty}\frac{dx}{\sqrt{x^{7}}e^{x}}$?

Published on 02 Apr 2016 - 15:10

score 66 · Answer 5 · 2026-03-31 22:49:23

66

Views

How to prove the product representation of Baenes G-function?

Published on 31 Mar 2026 - 22:49

score 38 · Answer 6 · 2026-02-24 03:06:07

38

Views

How to prove $\sum_{n\geq 0}{\frac{\Gamma(n+2+\alpha)}{n!\Gamma(2+\alpha)}z^n}=\frac{1}{(1-z)^{2+\alpha}}$

Published on 24 Feb 2026 - 3:06

score 152 · Answer 7 · 2016-04-04 06:01:34

152

Views

Gamma duplication formula via Hadamard

Published on 04 Apr 2016 - 6:01

score 226 · Answer 8 · 2016-04-05 14:27:40

226

Views

Infinite sum over Gamma functions?

Published on 05 Apr 2016 - 14:27

score 395 · Answer 9 · 2026-03-27 16:20:03

395

Views

Write area in terms of Gamma function

Published on 27 Mar 2026 - 16:20

score 1.8k · Answer 10 · 2016-04-05 19:17:30

1.8k

Views

Show that the second derivative $\Gamma''(x)$ is positive when $x>0$

Published on 05 Apr 2016 - 19:17

score 479 · Answer 11 · 2026-03-30 13:57:34

479

Views

What is $\int_{0}^{\infty}\frac{\cos^{n}x \sin x \ln x}{x} dx$?

Published on 30 Mar 2026 - 13:57

score 49 · Answer 12 · 2026-04-02 07:42:03

49

Views

Gamma representation of certain sequence

Published on 02 Apr 2026 - 7:42

score 1.5k · Answer 13 · 2016-04-07 15:47:51

1.5k

Views

Upper bound on ratio of incomplete Gamma function and Gamma function $\frac{ \Gamma \left( x; a\right)}{\Gamma(x)}$

Published on 07 Apr 2016 - 15:47

score 338 · Answer 14 · 2016-04-07 18:48:08

338

Views

Asymptotic behavior of an integral involving the gamma function

Published on 07 Apr 2016 - 18:48

score 76 · Answer 15 · 2016-04-08 16:40:05

76

Views

$\int_{-\infty}^{\infty} e^{-(x^2-2)^2-(\frac{1}{x^2}-2)^2}dx$

Published on 08 Apr 2016 - 16:40

List Question

Show that $\frac{\Gamma(n+k)}{\Gamma(n)}\sim n^k$ for large values of n

Evaluating the integral $\int_{-\infty}^{\infty} \frac{(1-ix)^{n-s_1}}{(1+ix)^{n+s_2}} dx$.

Sum of Gamma functions (product pairs)

How to calculate $\int_{0}^{\infty}\frac{dx}{\sqrt{x^{7}}e^{x}}$?

How to prove the product representation of Baenes G-function?

How to prove $\sum_{n\geq 0}{\frac{\Gamma(n+2+\alpha)}{n!\Gamma(2+\alpha)}z^n}=\frac{1}{(1-z)^{2+\alpha}}$

Gamma duplication formula via Hadamard

Infinite sum over Gamma functions?

Write area in terms of Gamma function

Show that the second derivative $\Gamma''(x)$ is positive when $x>0$

What is $\int_{0}^{\infty}\frac{\cos^{n}x \sin x \ln x}{x} dx$?

Gamma representation of certain sequence

Upper bound on ratio of incomplete Gamma function and Gamma function $\frac{ \Gamma \left( x; a\right)}{\Gamma(x)}$

Asymptotic behavior of an integral involving the gamma function

$\int_{-\infty}^{\infty} e^{-(x^2-2)^2-(\frac{1}{x^2}-2)^2}dx$

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