List questions from special-functions

Published on 12 Apr 2014 - 8:08

408

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$\frac{5\pi^3}{154}=\int_{\pi/6}^{\pi/2}\bigg[\Re\big(\text{Li}_2(4\sin^2\theta)\big) +\text{Li}_2\bigg(\frac{1}{4\sin^2\theta}\bigg) \bigg]d\theta$

Published on 13 Apr 2014 - 13:55

466

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bessel function maximizer

Published on 13 Apr 2014 - 14:35

399

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Sums Involving the Mobius Function

Published on 15 Apr 2014 - 3:26

18.2k

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How do you shift a sigmoidal curve to the right?

Published on 16 Apr 2014 - 7:34

45

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Are we only knowing prime counting function's property but not its infinite expansion?

Published on 16 Apr 2014 - 17:54

276

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Hypergeometric Function simple identity

Published on 27 Mar 2026 - 18:07

745

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Integral$=-\frac{4}{3}\log^3 2-\frac{\pi^2}{3}\log 2+\frac{5}{2}\zeta(3)$

Published on 18 Apr 2014 - 0:21

169

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Series $\sum_{n=0}^\infty (-1)^n \frac{x^{4n+1}}{4n+1}$

Published on 18 Apr 2014 - 1:52

2.6k

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Bessel Equations Addition Formula

Published on 18 Apr 2014 - 4:24

5.2k

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Reference Book on Special Functions

Published on 29 Mar 2026 - 4:01

53

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Asymptotic behaviour of $\frac{\Gamma(n)}{\Gamma(n+\frac{6}{5}+i\frac{2}{7})}$

Published on 20 Apr 2014 - 14:15

254

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Legendre associated functions

Published on 20 Apr 2014 - 23:59

116

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Properties of a Mehler's type integral

Published on 22 Apr 2014 - 0:37

1.7k

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Associated Legendre functions special values

Published on 22 Apr 2014 - 1:25

List Question

Zoo of sigmoid integrals (computational convenience)

$\frac{5\pi^3}{154}=\int_{\pi/6}^{\pi/2}\bigg[\Re\big(\text{Li}_2(4\sin^2\theta)\big) +\text{Li}_2\bigg(\frac{1}{4\sin^2\theta}\bigg) \bigg]d\theta$

bessel function maximizer

Sums Involving the Mobius Function

How do you shift a sigmoidal curve to the right?

Are we only knowing prime counting function's property but not its infinite expansion?

Hypergeometric Function simple identity

Integral$=-\frac{4}{3}\log^3 2-\frac{\pi^2}{3}\log 2+\frac{5}{2}\zeta(3)$

Series $\sum_{n=0}^\infty (-1)^n \frac{x^{4n+1}}{4n+1}$

Bessel Equations Addition Formula

Reference Book on Special Functions

Asymptotic behaviour of $\frac{\Gamma(n)}{\Gamma(n+\frac{6}{5}+i\frac{2}{7})}$

Legendre associated functions

Properties of a Mehler's type integral

Associated Legendre functions special values

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