Question

Integral involving Gauss Hypergeometric function, power, exponential and Bessel Function

score 377 · Answer 1 · 2013-05-13 14:41:23

377

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Integral involving Gauss Hypergeometric function, power, exponential and Bessel Function

Published on 13 May 2013 - 14:41

score 2.9k · Answer 2 · 2026-04-09 05:53:35

2.9k

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An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$

Published on 09 Apr 2026 - 5:53

score 389 · Answer 3 · 2013-05-14 01:05:19

389

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Find local maxima of this quadratic function

Published on 14 May 2013 - 1:05

score 1.3k · Answer 4 · 2026-04-07 03:35:01

1.3k

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A closed-form expression for the integral $\int_0^\infty\text{Ci}^{3}(x) \, \mathrm dx$

Published on 07 Apr 2026 - 3:35

score 180 · Answer 5 · 2026-03-30 01:47:07

180

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Integrate $\int_0^1 \Bigl(\mathrm{Li}_2\bigl(\frac{x-1}{x}\bigr)\Bigr)^2 \mathrm{d}x$

Published on 30 Mar 2026 - 1:47

score 84 · Answer 6 · 2026-04-06 17:51:45

84

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Show that $\int_0^t\!\!\left(t^2-x^2\right)^n\mathbb{d}x=\frac{\sqrt{\pi}}{2}t^{2n+1}\frac{\Gamma(n+1)}{\Gamma(n+\frac{3}{2})}$

Published on 06 Apr 2026 - 17:51

score 213 · Answer 7 · 2026-03-28 07:16:40

213

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The Tribonacci constant and the Dragon

Published on 28 Mar 2026 - 7:16

score 744 · Answer 8 · 2026-03-27 03:41:51

744

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Integral identity with square of Jacobi polynomial

Published on 27 Mar 2026 - 3:41

score 3k · Answer 9 · 2013-05-15 13:15:24

3k

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Difference between Rician distribution and Gaussian distribution

Published on 15 May 2013 - 13:15

score 258 · Answer 10 · 2026-04-07 03:35:52

258

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What type of Hypergeometric series is this?

Published on 07 Apr 2026 - 3:35

score 90 · Answer 11 · 2013-05-16 09:25:00

90

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Recurrence inequality for Dirichlet's eta function.

Published on 16 May 2013 - 9:25

score 46 · Answer 12 · 2013-05-16 09:33:16

46

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Square equivalent of $circ(r)$

Published on 16 May 2013 - 9:33

score 14.6k · Answer 13 · 2013-05-16 10:43:57

14.6k

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Integral of product of Bessel functions of the first kind

Published on 16 May 2013 - 10:43

score 417 · Answer 14 · 2013-05-16 16:29:35

417

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Convolution of $1/(1+x^2)$ and $\exp(-x^2/(4t))$

Published on 16 May 2013 - 16:29

score 4.6k · Answer 15 · 2026-04-09 07:07:29

4.6k

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Fourier Transforms of shifted sinc funtions

Published on 09 Apr 2026 - 7:07

List Question

Integral involving Gauss Hypergeometric function, power, exponential and Bessel Function

An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$

Find local maxima of this quadratic function

A closed-form expression for the integral $\int_0^\infty\text{Ci}^{3}(x) \, \mathrm dx$

Integrate $\int_0^1 \Bigl(\mathrm{Li}_2\bigl(\frac{x-1}{x}\bigr)\Bigr)^2 \mathrm{d}x$

Show that $\int_0^t\!\!\left(t^2-x^2\right)^n\mathbb{d}x=\frac{\sqrt{\pi}}{2}t^{2n+1}\frac{\Gamma(n+1)}{\Gamma(n+\frac{3}{2})}$

The Tribonacci constant and the Dragon

Integral identity with square of Jacobi polynomial

Difference between Rician distribution and Gaussian distribution

What type of Hypergeometric series is this?

Recurrence inequality for Dirichlet's eta function.

Square equivalent of $circ(r)$

Integral of product of Bessel functions of the first kind

Convolution of $1/(1+x^2)$ and $\exp(-x^2/(4t))$

Fourier Transforms of shifted sinc funtions

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