List questions from special-functions

Published on 19 Oct 2018 - 21:36

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Finding the limit of an expression involving two Lerch transcendent functions

Published on 20 Oct 2018 - 11:45

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Solution of equation $y''+x^2y=0$

Published on 27 Mar 2026 - 16:47

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On $s(\alpha)=\int_{0}^{\pi/2}\sin^{\alpha}(t)dt$

Published on 22 Oct 2018 - 3:22

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Compute Infinite sum of Zero Order modified Bessel Function with COS

Published on 26 Mar 2026 - 22:17

102

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Repeated rescaling of differential equations

Published on 23 Oct 2018 - 18:10

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The sum of infinite sum of modified Bessel function

Published on 26 Mar 2026 - 22:14

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Algorithm for solving a large class of linear 2nd order ODEs with polynomial coefficients.

Published on 24 Oct 2018 - 16:31

169

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How do we prove that $\int_{0}^{\pi/2}\sin(t)^{2n+3}dt=\frac{4^n(2n+2)}{(2n+3)(2n+1){2n\choose n}}$?

Published on 25 Mar 2026 - 10:25

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define an infinitely differentiable function that maps different sizes interval in same size intervals.

Published on 26 Oct 2018 - 14:52

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$\int_0^x\sin^a(t)\cos^b(t)dt=$?

Published on 27 Oct 2018 - 21:22

754

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Limit of a Bessel function is a Gaussian

Published on 27 Mar 2026 - 0:02

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If $a,b,c$ are positive integers with $c\leq a+b,$ can I conclude that $_2F_1(a,b;c;1)$ diverges?

Published on 26 Mar 2026 - 11:00

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Simplify $\sum_{l=0}^\infty \sum_{r=0}^\infty\frac{\Gamma(L+r-2q)}{\Gamma(L+r-1+2q)} \frac{\Gamma(L+r+l-1+2q)}{\Gamma(L+r+l+2)}\frac{r+1}{r+l+2}$

Published on 27 Mar 2026 - 1:00

78

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Closed form of Harmonic series without digits 9 in its decimal representation

Published on 31 Oct 2018 - 0:20

List Question

$\int_{1}^{\infty}t^{k-n}dt=\frac{1}{n-k-1}$?

Finding the limit of an expression involving two Lerch transcendent functions

Solution of equation $y''+x^2y=0$

On $s(\alpha)=\int_{0}^{\pi/2}\sin^{\alpha}(t)dt$

Compute Infinite sum of Zero Order modified Bessel Function with COS

Repeated rescaling of differential equations

The sum of infinite sum of modified Bessel function

Algorithm for solving a large class of linear 2nd order ODEs with polynomial coefficients.

How do we prove that $\int_{0}^{\pi/2}\sin(t)^{2n+3}dt=\frac{4^n(2n+2)}{(2n+3)(2n+1){2n\choose n}}$?

define an infinitely differentiable function that maps different sizes interval in same size intervals.

$\int_0^x\sin^a(t)\cos^b(t)dt=$?

Limit of a Bessel function is a Gaussian

If $a,b,c$ are positive integers with $c\leq a+b,$ can I conclude that $_2F_1(a,b;c;1)$ diverges?

Simplify $\sum_{l=0}^\infty \sum_{r=0}^\infty\frac{\Gamma(L+r-2q)}{\Gamma(L+r-1+2q)} \frac{\Gamma(L+r+l-1+2q)}{\Gamma(L+r+l+2)}\frac{r+1}{r+l+2}$

Closed form of Harmonic series without digits 9 in its decimal representation

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