List questions from special-functions

Published on 30 Mar 2017 - 19:07

526

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What is the closed form of $\sum_{n\geq 1}(-1)^{n-1}\psi'(n)^2$?

Published on 25 Mar 2026 - 14:25

217

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The integral $\int_{-\infty}^\infty \frac{e^{-x^2}}{(1+e^x)^2} dx$.

Published on 26 Mar 2026 - 22:58

178

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From integral to hypergeometric series

Published on 30 Mar 2026 - 0:03

180

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How can I show this is equivalent to the error function of $x$?

Published on 27 Mar 2026 - 19:53

410

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Jacobian Elliptic Functions

Published on 26 Mar 2026 - 4:49

112

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Solving an equation without product log function (Lambert's W function)

Published on 26 Mar 2026 - 11:05

51

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Solving $x e^{-(x-\lambda)^2}=c$ for various $\lambda$

Published on 06 Apr 2017 - 2:43

302

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How this integral was evaluated using hypergeometric series?

Published on 30 Mar 2026 - 0:04

324

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An interesting pattern in the general solution of the $n$-th order ODE: $\frac{d^n y}{dx^n}+\alpha x\frac{dy}{dx}+\beta y=0$.

Published on 30 Mar 2026 - 0:05

303

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Proof for Generating function of Bessel function

Published on 30 Mar 2026 - 7:04

229

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How can I integrate $\int\sqrt{\frac{x^2+bx+c}{x^2+ex+f}}dx?$

Published on 31 Jan 2023 - 23:47

222

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Integral power of error function with exponential

Published on 27 Mar 2026 - 19:51

119

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Integral of Hypergeometric series

Published on 30 Mar 2026 - 0:03

250

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How to compute the integral $\int^{\infty}_{-\infty}\Phi\left(x\right)\left[1-\Phi\left(\frac{x-\mu}{\sigma}\right)\right]\mathrm{d}x$

Published on 27 Mar 2026 - 19:53

List Question

Prove that $a\geq0$, when $f(x)=x^{3}+ax$ is (strictly) increasing.

What is the closed form of $\sum_{n\geq 1}(-1)^{n-1}\psi'(n)^2$?

The integral $\int_{-\infty}^\infty \frac{e^{-x^2}}{(1+e^x)^2} dx$.

From integral to hypergeometric series

How can I show this is equivalent to the error function of $x$?

Jacobian Elliptic Functions

Solving an equation without product log function (Lambert's W function)

Solving $x e^{-(x-\lambda)^2}=c$ for various $\lambda$

How this integral was evaluated using hypergeometric series?

An interesting pattern in the general solution of the $n$-th order ODE: $\frac{d^n y}{dx^n}+\alpha x\frac{dy}{dx}+\beta y=0$.

Proof for Generating function of Bessel function

How can I integrate $\int\sqrt{\frac{x^2+bx+c}{x^2+ex+f}}dx?$

Integral power of error function with exponential

Integral of Hypergeometric series

How to compute the integral $\int^{\infty}_{-\infty}\Phi\left(x\right)\left[1-\Phi\left(\frac{x-\mu}{\sigma}\right)\right]\mathrm{d}x$

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