List questions from special-functions

Published on 23 Feb 2026 - 15:10

44

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Some generalised combinatorial formula concerning the integral over a square of Gegenbauer Polynomials

Published on 26 Mar 2026 - 6:25

63

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Kummer's Fourier expansion for $\ln\Gamma(x)$ derivation: cosine integral series expansion

Published on 14 May 2023 - 13:10

258

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Compute integral $\int^\infty_{-\infty}\frac{1}{\big(\frac89x^2+\frac23\big)\sqrt{\frac{x^2}{3}+1}}~dx$

Published on 15 May 2023 - 22:16

84

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Are these smooth bump functions $\in C_{0}^{\infty}(-1,\ 1)$? $f(x) = \left(1+\exp\left(\frac{1-2|x|}{x^2-|x|}\right)\right)^{-1}$ and related

Published on 25 Mar 2026 - 20:11

77

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How to derive this polylogarithm identity (involving Bernoulli polynomials)?

Published on 23 Feb 2026 - 2:55

268

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On the binomial coefficient $\binom{-1}{-1}$

Published on 20 May 2023 - 21:24

187

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Show that $I>\phi$ a delightful integral inequality

Published on 03 Apr 2026 - 5:55

71

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Explicit bound for a definite integral

Published on 02 Apr 2026 - 0:56

259

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Question about the "nowhere analyticity" of the Fabius function

Published on 26 Mar 2026 - 6:32

27

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Proof product propriety of bessel function

Published on 25 Mar 2026 - 23:56

113

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Defining Higher Order Functions Satisfying $f^n+g^n=1$

Published on 02 Jun 2023 - 22:05

118

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Inverse of a gamma function

Published on 27 Mar 2026 - 2:38

64

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Compute the integral $ \int_0^\infty e^{-u^\ell} u^m du $

Published on 03 Apr 2026 - 5:46

70

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Compute the integral $\int_0^\infty t^{3/\xi-1} e^{-t} \Gamma(\frac{2}{\xi},t) \ dt$

Published on 27 Mar 2026 - 2:35

List Question

Asymptotic expansion of Legendre functions at $x=-1$

Some generalised combinatorial formula concerning the integral over a square of Gegenbauer Polynomials

Kummer's Fourier expansion for $\ln\Gamma(x)$ derivation: cosine integral series expansion

Compute integral $\int^\infty_{-\infty}\frac{1}{\big(\frac89x^2+\frac23\big)\sqrt{\frac{x^2}{3}+1}}~dx$

Are these smooth bump functions $\in C_{0}^{\infty}(-1,\ 1)$? $f(x) = \left(1+\exp\left(\frac{1-2|x|}{x^2-|x|}\right)\right)^{-1}$ and related

How to derive this polylogarithm identity (involving Bernoulli polynomials)?

On the binomial coefficient $\binom{-1}{-1}$

Show that $I>\phi$ a delightful integral inequality

Explicit bound for a definite integral

Question about the "nowhere analyticity" of the Fabius function

Proof product propriety of bessel function

Defining Higher Order Functions Satisfying $f^n+g^n=1$

Inverse of a gamma function

Compute the integral $ \int_0^\infty e^{-u^\ell} u^m du $

Compute the integral $\int_0^\infty t^{3/\xi-1} e^{-t} \Gamma(\frac{2}{\xi},t) \ dt$

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