Question

If $f(x) = (x+c)!$ and $g(x) = (ax+c)!$, how can I write $g(x)$ based on $f(x)$?

score 58 · Answer 1 · 2020-08-07 14:52:30

58

Views

If $f(x) = (x+c)!$ and $g(x) = (ax+c)!$, how can I write $g(x)$ based on $f(x)$?

Published on 07 Aug 2020 - 14:52

score 80 · Answer 2 · 2020-08-08 10:16:21

80

Views

Hard problem :Prove that $f(x)<\frac{3}{2}x-\frac{1}{2}$

Published on 08 Aug 2020 - 10:16

score 36 · Answer 3 · 2026-03-26 11:18:24

36

Views

Writing $(a)_k*(a)_k$ as one Pochhammer Symbol or in terms of one Gamma ($\Gamma$) function?

Published on 26 Mar 2026 - 11:18

score 104 · Answer 4 · 2026-02-25 10:14:01

104

Views

A series convergence problem about Gamma function

Published on 25 Feb 2026 - 10:14

score 129 · Answer 5 · 2020-08-09 19:38:52

129

Views

How to express hypergeometric function $_3F_2(a,b,c;d,e;x) $ in terms of $_2F_1$ or $\Gamma$ functions?

Published on 09 Aug 2020 - 19:38

score 71 · Answer 6 · 2020-08-10 09:25:29

71

Views

Limit of hypergeometric function in proof of Gauss's summation formula

Published on 10 Aug 2020 - 9:25

score 1k · Answer 7 · 2026-03-27 00:04:41

1k

Views

Is there any meaning to this "Super Derivative" operation I invented?

Published on 27 Mar 2026 - 0:04

score 49 · Answer 8 · 2026-03-26 01:28:06

49

Views

Euler-Mascheroni constant as local minima of a function

Published on 26 Mar 2026 - 1:28

score 240 · Answer 9 · 2026-04-07 12:44:26

240

Views

Can anyone prove that gamma function is complex for complex inputs?

Published on 07 Apr 2026 - 12:44

score 66 · Answer 10 · 2020-08-14 15:27:55

66

Views

Indefinite integral $ \int \frac{\log\Gamma(\frac{x}{2})}{x^2}\,dx$

Published on 14 Aug 2020 - 15:27

score 82 · Answer 11 · 2026-04-04 03:21:39

82

Views

Good upper-bound (via special functions) for $\int_0^1(u-u^2)^{n/2}e^{-cu^2/2}du$ where $c \ge 0$ and $n$ is a large positive integer

Published on 04 Apr 2026 - 3:21

score 985 · Answer 12 · 2026-03-27 17:40:24

985

Views

Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$

Published on 27 Mar 2026 - 17:40

score 1.5k · Answer 13 · 2026-03-28 01:04:14

1.5k

Views

Gamma and Beta function proof

Published on 28 Mar 2026 - 1:04

score 186 · Answer 14 · 2026-03-25 23:36:13

186

Views

Evaluating an integral using the beta, gamma and digamma functions

Published on 25 Mar 2026 - 23:36

score 60 · Answer 15 · 2020-08-21 11:44:52

60

Views

How to prove this result? $\frac{\Gamma(1-n-a) \Gamma(1-\frac{n}{2})}{\Gamma(1-n) \Gamma(1 - \frac{n}{2} -a)} = 0$ if n is odd.

Published on 21 Aug 2020 - 11:44

List Question

If $f(x) = (x+c)!$ and $g(x) = (ax+c)!$, how can I write $g(x)$ based on $f(x)$?

Hard problem :Prove that $f(x)<\frac{3}{2}x-\frac{1}{2}$

Writing $(a)_k*(a)_k$ as one Pochhammer Symbol or in terms of one Gamma ($\Gamma$) function?

A series convergence problem about Gamma function

How to express hypergeometric function $_3F_2(a,b,c;d,e;x) $ in terms of $_2F_1$ or $\Gamma$ functions?

Limit of hypergeometric function in proof of Gauss's summation formula

Is there any meaning to this "Super Derivative" operation I invented?

Euler-Mascheroni constant as local minima of a function

Can anyone prove that gamma function is complex for complex inputs?

Indefinite integral $ \int \frac{\log\Gamma(\frac{x}{2})}{x^2}\,dx$

Good upper-bound (via special functions) for $\int_0^1(u-u^2)^{n/2}e^{-cu^2/2}du$ where $c \ge 0$ and $n$ is a large positive integer

Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$

Gamma and Beta function proof

Evaluating an integral using the beta, gamma and digamma functions

How to prove this result? $\frac{\Gamma(1-n-a) \Gamma(1-\frac{n}{2})}{\Gamma(1-n) \Gamma(1 - \frac{n}{2} -a)} = 0$ if n is odd.

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