Question

An interesting integral

score 76 · Answer 1 · 2020-04-22 11:16:58

76

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An interesting integral

Published on 22 Apr 2020 - 11:16

score 264 · Answer 2 · 2026-03-29 05:50:07

264

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Definite Integral of modified bessel function of second kind

Published on 29 Mar 2026 - 5:50

score 118 · Answer 3 · 2020-04-26 06:05:18

118

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How can I prove $\lim_{s\to 1^-}\sum_{n=0}^{\infty}\left(-1\right)^n\frac{\Gamma(1+ns)}{\Gamma(1+n)}=\frac{1}{2}$

Published on 26 Apr 2020 - 6:05

score 1.2k · Answer 4 · 2020-04-27 13:01:45

1.2k

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Has anyone seen the definition of "alpha function" from Wolfram MathWorld in cited references?

Published on 27 Apr 2020 - 13:01

score 69 · Answer 5 · 2026-03-26 19:39:40

69

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Proving continued fraction for $\frac{I_{\frac{p}{q}}\left(\frac{2}{q}\right)}{I_{1+\frac{p}{q}}\left(\frac{2}{q}\right)}$

Published on 26 Mar 2026 - 19:39

score 62 · Answer 6 · 2020-04-28 14:02:30

62

Views

$\int_{0}^{6} x^{\{x\}} d x $ where {} in the G.I.F

Published on 28 Apr 2020 - 14:02

score 42 · Answer 7 · 2026-03-29 04:11:48

42

Views

Bessel function giving incorrect result

Published on 29 Mar 2026 - 4:11

score 247 · Answer 8 · 2026-03-27 10:47:52

247

Views

Proving $\int_{0}^{\frac{\pi}{2}}\text{erf}(\sqrt{a}\cos(x))\text{erf}(\sqrt{a}\sin(x))\sin(2x)dx=\frac{e^{-a}-1+a}{a}$

Published on 27 Mar 2026 - 10:47

score 189 · Answer 9 · 2026-03-29 05:49:59

189

Views

Orthogonality of Bessel functions with different indices

Published on 29 Mar 2026 - 5:49

score 67 · Answer 10 · 2026-03-25 09:28:43

67

Views

Decomposition of $\psi^{(n)}(1)$ in terms of $\psi^{(n)}(k)$

Published on 25 Mar 2026 - 9:28

score 608 · Answer 11 · 2026-03-30 08:07:19

608

Views

What is the asymptotic form of the spherical Bessel function $j_{n}(x)$ when $n \to \infty$?

Published on 30 Mar 2026 - 8:07

score 257 · Answer 12 · 2026-03-29 07:32:12

257

Views

$K_{\frac{3}{2}}(z)=?$ where $K_{\nu}$ is the modified Bessel function

Published on 29 Mar 2026 - 7:32

score 40 · Answer 13 · 2026-03-29 07:30:33

40

Views

Expression of $\int_{\mathbb S^{n-1}}\, e^{-i\left<v,\omega\right>}\,d\sigma(\omega) = ?$

Published on 29 Mar 2026 - 7:30

score 41 · Answer 14 · 2020-05-08 06:11:58

41

Views

Power series summing $e^{-n + i n^2}$ over positive integers

Published on 08 May 2020 - 6:11

score 43 · Answer 15 · 2026-03-25 12:51:59

43

Views

$\sum_i^{\infty}e^{(-(2i+1)^2a)}(2i+1)^2$ where a is is a positive real number

Published on 25 Mar 2026 - 12:51

List Question

An interesting integral

Definite Integral of modified bessel function of second kind

How can I prove $\lim_{s\to 1^-}\sum_{n=0}^{\infty}\left(-1\right)^n\frac{\Gamma(1+ns)}{\Gamma(1+n)}=\frac{1}{2}$

Has anyone seen the definition of "alpha function" from Wolfram MathWorld in cited references?

Proving continued fraction for $\frac{I_{\frac{p}{q}}\left(\frac{2}{q}\right)}{I_{1+\frac{p}{q}}\left(\frac{2}{q}\right)}$

$\int_{0}^{6} x^{\{x\}} d x $ where {} in the G.I.F

Bessel function giving incorrect result

Proving $\int_{0}^{\frac{\pi}{2}}\text{erf}(\sqrt{a}\cos(x))\text{erf}(\sqrt{a}\sin(x))\sin(2x)dx=\frac{e^{-a}-1+a}{a}$

Orthogonality of Bessel functions with different indices

Decomposition of $\psi^{(n)}(1)$ in terms of $\psi^{(n)}(k)$

What is the asymptotic form of the spherical Bessel function $j_{n}(x)$ when $n \to \infty$?

$K_{\frac{3}{2}}(z)=?$ where $K_{\nu}$ is the modified Bessel function

Expression of $\int_{\mathbb S^{n-1}}\, e^{-i\left<v,\omega\right>}\,d\sigma(\omega) = ?$

Power series summing $e^{-n + i n^2}$ over positive integers

$\sum_i^{\infty}e^{(-(2i+1)^2a)}(2i+1)^2$ where a is is a positive real number

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