Question

An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$

score 37.6k · Answer 1 · 2026-04-07 14:43:58

37.6k

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An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$

Published on 07 Apr 2026 - 14:43

score 113 · Answer 2 · 2026-04-11 16:31:14

113

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Simplifying confluient hypergeometric functions

Published on 11 Apr 2026 - 16:31

score 769 · Answer 3 · 2026-04-01 10:00:24

769

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Showing that the Barnes G-function satisfies the functional equation $G(z+1) = \Gamma(z) G(z) $

Published on 01 Apr 2026 - 10:00

score 57 · Answer 4 · 2026-04-10 03:03:57

57

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How to find the non singular condition for this equation

Published on 10 Apr 2026 - 3:03

score 688 · Answer 5 · 2013-10-01 17:06:53

Prove $\gamma_1\left(\frac34\right)-\gamma_1\left(\frac14\right)=\pi\,\left(\gamma+4\ln2+3\ln\pi-4\ln\Gamma\left(\frac14\right)\right)$

score 81 · Answer 6 · 2013-10-02 11:08:02

81

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Function by properties

Published on 02 Oct 2013 - 11:08

score 588 · Answer 7 · 2026-04-07 14:43:38

588

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A closed form for $\int_0^1\frac{\ln(-\ln x)\ \operatorname{li}^2x}{x}dx$

Published on 07 Apr 2026 - 14:43

score 2.9k · Answer 8 · 2026-04-11 08:18:25

2.9k

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What is the relationship between hypergeometric function and Legendre polynomials?

Published on 11 Apr 2026 - 8:18

score 20k · Answer 9 · 2026-03-27 19:51:53

20k

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Relation between Beta and Gamma functions

Published on 27 Mar 2026 - 19:51

score 487 · Answer 10 · 2026-04-07 14:42:16

487

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Conjectural closed form for $\int_0^\infty\sqrt[3]z\ \operatorname{Ei}^2(-z)\,dz$

Published on 07 Apr 2026 - 14:42

score 1.2k · Answer 11 · 2013-10-04 19:45:33

1.2k

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Numerical approximation for log of incomplete beta function

Published on 04 Oct 2013 - 19:45

score 1.2k · Answer 12 · 2026-04-02 15:43:03

1.2k

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On Shanks' quartic approximation $\pi \approx \frac{6}{\sqrt{3502}}\ln(2u)$

Published on 02 Apr 2026 - 15:43

score 1.2k · Answer 13 · 2026-04-10 23:47:29

1.2k

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Identity using q-Pochhammer symbols

Published on 10 Apr 2026 - 23:47

score 23.7k · Answer 14 · 2026-04-09 23:31:22

23.7k

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How can a unit step function be differentiable??

Published on 09 Apr 2026 - 23:31

score 116 · Answer 15 · 2026-04-10 09:56:52

116

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Integral over a complex plane involving Laguerre polynomial

Published on 10 Apr 2026 - 9:56

List Question

An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$

Simplifying confluient hypergeometric functions

Showing that the Barnes G-function satisfies the functional equation $G(z+1) = \Gamma(z) G(z) $

How to find the non singular condition for this equation

Prove $\gamma_1\left(\frac34\right)-\gamma_1\left(\frac14\right)=\pi\,\left(\gamma+4\ln2+3\ln\pi-4\ln\Gamma\left(\frac14\right)\right)$

Function by properties

A closed form for $\int_0^1\frac{\ln(-\ln x)\ \operatorname{li}^2x}{x}dx$

What is the relationship between hypergeometric function and Legendre polynomials?

Relation between Beta and Gamma functions

Conjectural closed form for $\int_0^\infty\sqrt[3]z\ \operatorname{Ei}^2(-z)\,dz$

Numerical approximation for log of incomplete beta function

On Shanks' quartic approximation $\pi \approx \frac{6}{\sqrt{3502}}\ln(2u)$

Identity using q-Pochhammer symbols

How can a unit step function be differentiable??

Integral over a complex plane involving Laguerre polynomial

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