List questions from special-functions

Published on 25 Mar 2026 - 11:33

33

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Is there a closed form expression of $_3F_2\left(a,b,-\frac{1}{2};a-\frac{1}{2},a+b;1\right)$ where $a,b>0$?

Published on 28 Mar 2026 - 9:33

63

Views

Series of Kummer function works only with the third variable.

Published on 26 Mar 2026 - 18:58

879

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Recurrence relation for associated Laguerre Polynomials: same index and argument

Published on 06 Apr 2020 - 15:36

41

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Simplifying factorials in the Bessel polynomials

Published on 29 Mar 2026 - 2:29

91

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Reduction of ${}_{4}F_{3}(\cdots; 1)$

Published on 28 Mar 2026 - 11:22

193

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Sum of squared Fresnel sine integral

Published on 22 Mar 2026 - 11:25

94

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Integral involving Hypergeometric Function 2F1 and its derivative

Published on 28 Mar 2026 - 2:21

62

Views

How to prove $-J_0(\pi \mu) = J_2(\pi \mu)$ where $\mu$ is a solution of $J_1(\pi x) = 0$?

Published on 29 Mar 2026 - 3:36

36

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(Non-trivial) Fourier series coefficients

Published on 17 Apr 2020 - 7:20

51

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Solution of $f(x) = \mu x f'(x) + \lambda x f''(x)$

Published on 19 Apr 2020 - 14:34

156

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An inverse function for $-\log x/\log (1+x)$

Published on 23 Feb 2026 - 10:00

181

Views

How to simplify this polylog expression $\operatorname{Li}_4\left(\frac{z-1}{z}\right)$?

Published on 26 Mar 2026 - 13:02

381

Views

Value of $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n!}}$?

Published on 28 Mar 2026 - 9:33

170

Views

Integration related to Bessel function

Published on 30 Mar 2026 - 7:05

List Question

Sum of the first $1/n$-th powers of z, L-function with rational powers.

Is there a closed form expression of $_3F_2\left(a,b,-\frac{1}{2};a-\frac{1}{2},a+b;1\right)$ where $a,b>0$?

Series of Kummer function works only with the third variable.

Recurrence relation for associated Laguerre Polynomials: same index and argument

Simplifying factorials in the Bessel polynomials

Reduction of ${}_{4}F_{3}(\cdots; 1)$

Sum of squared Fresnel sine integral

Integral involving Hypergeometric Function 2F1 and its derivative

How to prove $-J_0(\pi \mu) = J_2(\pi \mu)$ where $\mu$ is a solution of $J_1(\pi x) = 0$?

(Non-trivial) Fourier series coefficients

Solution of $f(x) = \mu x f'(x) + \lambda x f''(x)$

An inverse function for $-\log x/\log (1+x)$

How to simplify this polylog expression $\operatorname{Li}_4\left(\frac{z-1}{z}\right)$?

Value of $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n!}}$?

Integration related to Bessel function

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