Question

Deriving the series representation of the digamma function from the functional equation

score 381 · Answer 1 · 2026-04-06 19:35:33

381

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Deriving the series representation of the digamma function from the functional equation

Published on 06 Apr 2026 - 19:35

score 721 · Answer 2 · 2013-07-17 13:06:31

721

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Upper bound for the quotient of gamma functions?

Published on 17 Jul 2013 - 13:06

score 68 · Answer 3 · 2026-04-06 09:34:02

68

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Non-equality with Gamma functions

Published on 06 Apr 2026 - 9:34

score 343 · Answer 4 · 2026-04-01 06:31:48

343

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The evaluation of the infinite product $\prod_{k=2}^{\infty} \frac{k^{2}-1}{k^{2}+1}$

Published on 01 Apr 2026 - 6:31

score 69 · Answer 5 · 2013-07-27 18:31:03

69

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Show that $\sum\limits_{k=0}^{y-1}(-1)^k\frac{\binom{y-1}{k}}{k+x}=\frac{(x-1)!(y-1)!}{(x+y-1)!}$.

Published on 27 Jul 2013 - 18:31

score 115.8k · Answer 6 · 2026-04-06 12:57:12

115.8k

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How do we calculate factorials for numbers with decimal places?

Published on 06 Apr 2026 - 12:57

score 9.4k · Answer 7 · 2026-04-06 12:03:32

9.4k

Views

Real and imaginary part of Gamma function

Published on 06 Apr 2026 - 12:03

score 476 · Answer 8 · 2026-04-06 12:55:17

476

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How Many Ways to Build a 6-Pack

Published on 06 Apr 2026 - 12:55

score 1k · Answer 9 · 2013-08-01 12:34:12

1k

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Big Gamma $\Gamma$ meets little gamma $\gamma$

Published on 01 Aug 2013 - 12:34

score 4.6k · Answer 10 · 2013-08-04 19:59:33

4.6k

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How to prove Gauss’s Multiplication Formula?

Published on 04 Aug 2013 - 19:59

score 491 · Answer 11 · 2013-08-05 12:30:55

491

Views

Prove $\Gamma\left(\frac{1}{2}\right)= \sqrt\pi$, using $\Gamma(p)\Gamma(1-p) = \frac{\pi}{\sin(\pi p)}$

Published on 05 Aug 2013 - 12:30

score 61 · Answer 12 · 2013-08-05 14:49:26

61

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Relation between two gamma functions

Published on 05 Aug 2013 - 14:49

score 111 · Answer 13 · 2013-08-06 09:31:16

111

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Why do we have $\psi^{(m)} (z)=(-1)^{m+1}\int_{0}^{\infty}\frac{t^me^{-zt}}{1-e^{-t}}dt$?

Published on 06 Aug 2013 - 9:31

score 157 · Answer 14 · 2026-03-27 06:12:42

157

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how to prove that $\psi_1(x)=\sum_{n=0}^{\infty}\frac{B_n}{x^{n+1}}$ ?

Published on 27 Mar 2026 - 6:12

score 500 · Answer 15 · 2013-08-09 01:44:21

500

Views

Estimate $\displaystyle\int_0^\infty\frac{t^n}{n!}e^{-e^t}dt$ accurately.

Published on 09 Aug 2013 - 1:44

List Question

Deriving the series representation of the digamma function from the functional equation

Upper bound for the quotient of gamma functions?

Non-equality with Gamma functions

The evaluation of the infinite product $\prod_{k=2}^{\infty} \frac{k^{2}-1}{k^{2}+1}$

Show that $\sum\limits_{k=0}^{y-1}(-1)^k\frac{\binom{y-1}{k}}{k+x}=\frac{(x-1)!(y-1)!}{(x+y-1)!}$.

How do we calculate factorials for numbers with decimal places?

Real and imaginary part of Gamma function

How Many Ways to Build a 6-Pack

Big Gamma $\Gamma$ meets little gamma $\gamma$

How to prove Gauss’s Multiplication Formula?

Prove $\Gamma\left(\frac{1}{2}\right)= \sqrt\pi$, using $\Gamma(p)\Gamma(1-p) = \frac{\pi}{\sin(\pi p)}$

Relation between two gamma functions

Why do we have $\psi^{(m)} (z)=(-1)^{m+1}\int_{0}^{\infty}\frac{t^me^{-zt}}{1-e^{-t}}dt$?

how to prove that $\psi_1(x)=\sum_{n=0}^{\infty}\frac{B_n}{x^{n+1}}$ ?

Estimate $\displaystyle\int_0^\infty\frac{t^n}{n!}e^{-e^t}dt$ accurately.

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