List questions from special-functions

Published on 16 Sep 2015 - 8:25

531

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Sigmoid function increasing for large values of variable x

Published on 16 Sep 2015 - 14:29

2.8k

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complex conjugate of Bessel function

Published on 01 Apr 2026 - 6:27

220

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PDE $(\partial_{tt}+a\partial_t-b\nabla^2)f(r,t)=0$

Published on 16 Sep 2015 - 23:21

413

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Simplifying a certain polylogarithmic sum in two variables

Published on 27 Mar 2026 - 17:05

57

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Have the derivative of a function as a recurrence, looking for a closed form expression of the function.

Published on 17 Sep 2015 - 15:34

44

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Functions that sum to zero under cyclic index permutations?

Published on 17 Sep 2015 - 16:05

119

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complex infinity

Published on 01 Apr 2026 - 6:23

2.1k

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Legendre functions $Q_n(x)$ of the second kind

Published on 26 Mar 2026 - 19:01

4.2k

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Solution of an integral with strange imprecision of gamma functions

Published on 05 Apr 2026 - 11:03

29

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Seeking a 3 variable function with a specific property

Published on 18 Sep 2015 - 10:02

899

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Derive the Differential Equation for Laguerre polynomials

Published on 18 Sep 2015 - 12:24

351

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Prove that $\int_0^\infty\frac{x\cos(x)-\sin(x)}{x\left({e^x}-1\right)}\,dx = \frac{\pi}2+\arg\left(\Gamma(i)\right)-\Re\left(\psi_0(i)\right)$

Published on 05 Apr 2026 - 9:04

1.4k

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$(\partial_{tt}-\nabla^2+\partial_t)f=g,\quad (\partial_t-\nabla^2+b)g=\partial_t f$

Published on 18 Sep 2015 - 21:58

304

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Given a Fourier series $f(x)$: What's the difference between the value the expansion takes for given $x$ and the value it converges to for given $x$?

Published on 20 Sep 2015 - 5:36

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Restrict solutions using lambert W to reals

Sigmoid function increasing for large values of variable x

complex conjugate of Bessel function

PDE $(\partial_{tt}+a\partial_t-b\nabla^2)f(r,t)=0$

Simplifying a certain polylogarithmic sum in two variables

Have the derivative of a function as a recurrence, looking for a closed form expression of the function.

Functions that sum to zero under cyclic index permutations?

complex infinity

Legendre functions $Q_n(x)$ of the second kind

Solution of an integral with strange imprecision of gamma functions

Seeking a 3 variable function with a specific property

Derive the Differential Equation for Laguerre polynomials

Prove that $\int_0^\infty\frac{x\cos(x)-\sin(x)}{x\left({e^x}-1\right)}\,dx = \frac{\pi}2+\arg\left(\Gamma(i)\right)-\Re\left(\psi_0(i)\right)$

$(\partial_{tt}-\nabla^2+\partial_t)f=g,\quad (\partial_t-\nabla^2+b)g=\partial_t f$

Given a Fourier series $f(x)$: What's the difference between the value the expansion takes for given $x$ and the value it converges to for given $x$?

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