List questions from special-functions

Published on 11 Apr 2026 - 0:26

218

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Finding a closed-form for the sum $\sum_{n=1}^{\infty}\frac{\left(-1\right)^{n}H_{2n}}{n^{4}}$

Published on 16 Apr 2026 - 21:15

232

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Are there non-integer $\nu$, such that the Parabolic Cylinder Function vanishes as $z \to -\infty$?

Published on 10 Apr 2026 - 19:13

61

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How can I find a function with the following characteristics?

Published on 11 Apr 2026 - 3:26

435

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Sum with Digamma function expressed by hypergeometric function?

Published on 12 Apr 2026 - 17:29

272

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Generalization of Gamma function

Published on 15 Apr 2026 - 14:13

97

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Solving an ODE $\psi''(x) + \left[a^2 - x^{2n}\right]\psi(x) = 0$ for $n\in \mathbb{Z}$ and $a\in \mathbb{R}$.

Published on 17 Apr 2026 - 6:32

126

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How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

Published on 14 Apr 2026 - 14:12

97

Views

Another way to write $ \frac{\Gamma(\frac{1}{2}-x)}{\Gamma(x)} $

Published on 15 Apr 2026 - 19:50

482

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Integral in terms of the modified Bessel function of the second kind

Published on 12 Apr 2026 - 16:01

253

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How to rewrite $\int\limits_A^B \frac{x^n \exp(-\alpha x)}{\small(x + \beta\small)^m} \, dx$?

Published on 16 Apr 2026 - 3:18

116

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Computing $\int_0^1dx\:I_0(\alpha \sqrt{1-x})e^{\beta x}$

Published on 16 Apr 2026 - 15:14

63

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Computation of Bessel-like integral

Published on 13 Apr 2026 - 1:26

375

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Does $\mathrm{\int W(ln(x))dx}$ have a closed form?

Published on 13 Apr 2026 - 11:30

51

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Identity in Gradsteyn & Rhyzik

Published on 13 Apr 2026 - 0:15

List Question

Series and integral transforms in Python

Finding a closed-form for the sum $\sum_{n=1}^{\infty}\frac{\left(-1\right)^{n}H_{2n}}{n^{4}}$

Are there non-integer $\nu$, such that the Parabolic Cylinder Function vanishes as $z \to -\infty$?

How can I find a function with the following characteristics?

Sum with Digamma function expressed by hypergeometric function?

Generalization of Gamma function

Solving an ODE $\psi''(x) + \left[a^2 - x^{2n}\right]\psi(x) = 0$ for $n\in \mathbb{Z}$ and $a\in \mathbb{R}$.

How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

Another way to write $ \frac{\Gamma(\frac{1}{2}-x)}{\Gamma(x)} $

Integral in terms of the modified Bessel function of the second kind

How to rewrite $\int\limits_A^B \frac{x^n \exp(-\alpha x)}{\small(x + \beta\small)^m} \, dx$?

Computing $\int_0^1dx\:I_0(\alpha \sqrt{1-x})e^{\beta x}$

Computation of Bessel-like integral

Does $\mathrm{\int W(ln(x))dx}$ have a closed form?

Identity in Gradsteyn & Rhyzik

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