List questions from special-functions

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On Jacobi theta functions and some curious evaluations

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Published on 08 Apr 2026 - 15:54

189

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Hermite Polynomials for |x|

Published on 25 Apr 2026 - 9:52

97

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The integral of $(1+x^2)^{-a} \ln (1+x^2)$

Published on 16 Apr 2026 - 11:56

457

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Infinite products $f(x) = \prod_{n=1}^{\infty}(1-x^n)$ and $g(x) = \prod_{n=1}^{\infty}(1+x^n)$

Published on 17 Apr 2026 - 11:33

116

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Reexpressing an Integral Involving Bessel Function

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370

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Proof of Bonnet's Recursion Formula for Legendre Functions of the Second Kind?

Published on 03 May 2026 - 18:15

106

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How to prove that $ \ln{G(z+n)}+\ln{Γ(z+n)}=\ln{G(z)} +(n+1)\ln{Γ(z)}+\displaystyle \sum_{k=1}^{n} k\ln(z+n-k) $?

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101

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Integral of product of Bessel functions of the first kind

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39

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Recurrence relation for hypergeometric function

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233

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How to solve $\int\frac{x\arctan x}{x^4+1}dx$ in a practical way

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226

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The $n$th derivative of the $n$th spherical Bessel function

Published on 16 Apr 2026 - 3:36

75

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Solve $\int_0^1\frac{x(x+1)^b}{\alpha-x}dx$ using hypergeometric functions

Published on 16 Apr 2026 - 5:19

List Question

Closed form for infinite sum over Hermite polynomial $H_{2n}$

On Jacobi theta functions and some curious evaluations

How to find the asymptotic expansion of error function at infinity?

How to evaluate $\int\frac{x^ndx}{\sqrt{ax^2+bx+c}}$ for natural $n$

Hermite Polynomials for |x|

The integral of $(1+x^2)^{-a} \ln (1+x^2)$

Infinite products $f(x) = \prod_{n=1}^{\infty}(1-x^n)$ and $g(x) = \prod_{n=1}^{\infty}(1+x^n)$

Reexpressing an Integral Involving Bessel Function

Proof of Bonnet's Recursion Formula for Legendre Functions of the Second Kind?

How to prove that $ \ln{G(z+n)}+\ln{Γ(z+n)}=\ln{G(z)} +(n+1)\ln{Γ(z)}+\displaystyle \sum_{k=1}^{n} k\ln(z+n-k) $?

Integral of product of Bessel functions of the first kind

Recurrence relation for hypergeometric function

How to solve $\int\frac{x\arctan x}{x^4+1}dx$ in a practical way

The $n$th derivative of the $n$th spherical Bessel function

Solve $\int_0^1\frac{x(x+1)^b}{\alpha-x}dx$ using hypergeometric functions

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