List questions from special-functions

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Deriving Rodrigues Formula and Generating function of Hermite Polynomial from $H_n(x)= e^{x^2/2}(x-\frac{d}{dx})^ne^{-x^2/2}$

Published on 25 Mar 2026 - 8:06

243

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Are there functions that satisfy the following properties?

Published on 13 Jun 2018 - 4:12

448

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Mean of Beta distribution without using Gamma function?

Published on 25 Mar 2026 - 5:57

82

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Closed form for infinite series $\sum_{n=1}^\infty \prod_{j=1}^n \left[1-(\tfrac{j}{n}u+v)^2\right]^{-1} x^n$

Published on 25 Mar 2026 - 11:20

167

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One-half shift in argument of Dedekind eta function

Published on 26 Mar 2026 - 16:57

865

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Advantage of Bernstein polynomial basis

Published on 25 Mar 2026 - 0:06

223

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A lower bound for the Riemann zeta function

Published on 19 Jun 2018 - 14:50

894

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Integral of product of spherical Bessel function of first kind with the second

Published on 25 Mar 2026 - 23:52

250

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Indefinite integral involving Spherical Bessel function of second kind

Published on 25 Mar 2026 - 23:53

121

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Integral representation of Bessel functions

Published on 26 Mar 2026 - 13:50

151

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Gamma function results

Published on 25 Mar 2026 - 20:09

432

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Simplifying incomplete beta function

Published on 25 Mar 2026 - 7:23

319

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Evaluating $\int_0^\infty \frac{\arctan x\operatorname{Li}_2( -x )}{x^2} \, dx$

Published on 24 Jun 2018 - 7:31

1.3k

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How are values of the Dirichlet Beta function derivative derived?

Published on 25 Mar 2026 - 1:22

879

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How can we convert double sums to single sums?

Published on 29 Jun 2018 - 0:15

List Question

Deriving Rodrigues Formula and Generating function of Hermite Polynomial from $H_n(x)= e^{x^2/2}(x-\frac{d}{dx})^ne^{-x^2/2}$

Are there functions that satisfy the following properties?

Mean of Beta distribution without using Gamma function?

Closed form for infinite series $\sum_{n=1}^\infty \prod_{j=1}^n \left[1-(\tfrac{j}{n}u+v)^2\right]^{-1} x^n$

One-half shift in argument of Dedekind eta function

Advantage of Bernstein polynomial basis

A lower bound for the Riemann zeta function

Integral of product of spherical Bessel function of first kind with the second

Indefinite integral involving Spherical Bessel function of second kind

Integral representation of Bessel functions

Gamma function results

Simplifying incomplete beta function

Evaluating $\int_0^\infty \frac{\arctan x\operatorname{Li}_2( -x )}{x^2} \, dx$

How are values of the Dirichlet Beta function derivative derived?

How can we convert double sums to single sums?

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