Question

Sum of Fermi-Dirac integrals with opposite chemical potentials: closed form (Le Bellac eq. 1.13)

score 120 · Answer 1 · 2026-03-25 12:20:35

120

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Sum of Fermi-Dirac integrals with opposite chemical potentials: closed form (Le Bellac eq. 1.13)

Published on 25 Mar 2026 - 12:20

score 70 · Answer 2 · 2026-03-28 14:44:15

70

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Calculate $\lim_{s\rightarrow \infty}\frac{\sqrt{s}\Gamma(2s+1)}{(2^s\Gamma(s+1))^2}$

Published on 28 Mar 2026 - 14:44

score 316 · Answer 3 · 2026-04-08 18:26:43

316

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How to convert Gamma distribution into Chi square distribution?

Published on 08 Apr 2026 - 18:26

score 117 · Answer 4 · 2026-03-28 14:44:27

117

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Which equations can be solved by Boost C++ library’s ibeta_inva, ibeta_invb, and gamma_q_inva functions?

Published on 28 Mar 2026 - 14:44

score 1.6k · Answer 5 · 2026-04-12 13:03:13

1.6k

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How can construction of the gamma function be motivated?

Published on 12 Apr 2026 - 13:03

score 118 · Answer 6 · 2026-04-12 22:52:16

118

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Why do we split the gamma function at x=1?

Published on 12 Apr 2026 - 22:52

score 382 · Answer 7 · 2022-02-16 02:12:26

382

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How to get $\int_0^∞\frac{dx}{(x^2+1)^n}=\frac{(2n-3)!!}{(2n-2)!!}\frac{\pi}{2}\overset{?}=\frac{\sqrt{\pi}}{2}\frac{Γ(n-\frac{1}{2})}{Γ(n)}$?

Published on 16 Feb 2022 - 2:12

score 147 · Answer 8 · 2026-04-12 12:22:59

147

Views

Upper bound for L-series of modular form from its integral representation

Published on 12 Apr 2026 - 12:22

score 142 · Answer 9 · 2026-04-13 07:53:10

142

Views

A question on (trigonometric) prime counting function and twin prime counting function

Published on 13 Apr 2026 - 7:53

score 129 · Answer 10 · 2026-04-11 09:30:06

129

Views

An inequality regarding Beta function/Gamma functions.

Published on 11 Apr 2026 - 9:30

score 56 · Answer 11 · 2026-04-08 07:36:16

56

Views

Extension of the exponential power series to an integral

Published on 08 Apr 2026 - 7:36

score 99 · Answer 12 · 2022-02-24 21:15:29

99

Views

If $\Gamma$ is differentiable on $(0,\infty)$, then it is differentiable on whole $\mathbb{R}\setminus \{0,-1,-2,\dots\}$.

Published on 24 Feb 2022 - 21:15

score 407 · Answer 13 · 2026-04-12 04:20:23

407

Views

The limit form representation of gamma function

Published on 12 Apr 2026 - 4:20

score 42 · Answer 14 · 2026-04-12 23:25:24

42

Views

About showing that $\Gamma'(x)\to -\infty$ as $x\to 0^+$

Published on 12 Apr 2026 - 23:25

score 74 · Answer 15 · 2026-04-10 21:08:55

74

Views

Conditions for 'extraordinary' natural numbers

Published on 10 Apr 2026 - 21:08

List Question

Sum of Fermi-Dirac integrals with opposite chemical potentials: closed form (Le Bellac eq. 1.13)

Calculate $\lim_{s\rightarrow \infty}\frac{\sqrt{s}\Gamma(2s+1)}{(2^s\Gamma(s+1))^2}$

How to convert Gamma distribution into Chi square distribution?

Which equations can be solved by Boost C++ library’s ibeta_inva, ibeta_invb, and gamma_q_inva functions?

How can construction of the gamma function be motivated?

Why do we split the gamma function at x=1?

How to get $\int_0^∞\frac{dx}{(x^2+1)^n}=\frac{(2n-3)!!}{(2n-2)!!}\frac{\pi}{2}\overset{?}=\frac{\sqrt{\pi}}{2}\frac{Γ(n-\frac{1}{2})}{Γ(n)}$?

Upper bound for L-series of modular form from its integral representation

A question on (trigonometric) prime counting function and twin prime counting function

An inequality regarding Beta function/Gamma functions.

Extension of the exponential power series to an integral

If $\Gamma$ is differentiable on $(0,\infty)$, then it is differentiable on whole $\mathbb{R}\setminus \{0,-1,-2,\dots\}$.

The limit form representation of gamma function

About showing that $\Gamma'(x)\to -\infty$ as $x\to 0^+$

Conditions for 'extraordinary' natural numbers

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