Newbetuts

Seeking closed form for infinite sum $\sum \limits_{ n=1 }^{ \infty }{ \frac { { \left(n! \right) }^{ 2 } }{ { n }^{ 3 }(2n)! } }$

Proving $\sqrt{1-x^2}\ge \operatorname{erf}(\sqrt{-\log x})$

Intriguing polynomials coming from a combinatorial physics problem

(New Solution needed) Explicit series expansion for inverse of $e^{-x}\left(\frac{x^2}2+x+1\right)$

How to prove that $\frac{\eta^{14}(q^4)}{\eta^{4}(q^8)}=4\eta^4(q^2)\eta^2(q^4)\eta^4(q^8)+\eta^4(q)\eta^2(q^2)\eta^4(q^4)$?

Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$

Special Gamma function integral

$\sum_{n\geq 1}\frac{(-1)^n \ln n}{n}$

How can I evaluate $\int_{-\infty}^{\infty}\frac{e^{-x^2}(2x^2-1)}{1+x^2}dx$?

How to find a function mapping matrix indices?

What is this series relating to the residues of the Gamma function?

Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.

Evaluating the elliptic integral $\int_{-\pi}^\pi\frac{dx}{\sqrt{(t-2\cos x)^2-4}}$

Ramanujan Summation

Calculate the following integral $\int_0^{\pi/2} \frac{\sin^m x\,\mathrm{d}x}{\sin x + \cos x}$, $m=2k-1$

How are values of the Dirichlet Beta function derivative derived?

Can $\Gamma(1/5)$ be written in this form?

New posts in special-functions

Iterative refinement algorithm for computing exp(x) with arbitrary precision

On the integral $\int_{0}^{1/2}\frac{\text{Li}_3(1-z)}{\sqrt{z(1-z)}}\,dz$

Bessel's Differential Equation - textbook queries:

Seeking closed form for infinite sum $\sum \limits_{ n=1 }^{ \infty }{ \frac { { \left(n! \right) }^{ 2 } }{ { n }^{ 3 }(2n)! } }$

Proving $\sqrt{1-x^2}\ge \operatorname{erf}(\sqrt{-\log x})$

Intriguing polynomials coming from a combinatorial physics problem

(New Solution needed) Explicit series expansion for inverse of $e^{-x}\left(\frac{x^2}2+x+1\right)$

How to prove that $\frac{\eta^{14}(q^4)}{\eta^{4}(q^8)}=4\eta^4(q^2)\eta^2(q^4)\eta^4(q^8)+\eta^4(q)\eta^2(q^2)\eta^4(q^4)$?

Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$

Special Gamma function integral

$\sum_{n\geq 1}\frac{(-1)^n \ln n}{n}$

How can I evaluate $\int_{-\infty}^{\infty}\frac{e^{-x^2}(2x^2-1)}{1+x^2}dx$?

How to find a function mapping matrix indices?

What is this series relating to the residues of the Gamma function?

Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.

Evaluating the elliptic integral $\int_{-\pi}^\pi\frac{dx}{\sqrt{(t-2\cos x)^2-4}}$

Ramanujan Summation

Calculate the following integral $\int_0^{\pi/2} \frac{\sin^m x\,\mathrm{d}x}{\sin x + \cos x}$, $m=2k-1$

How are values of the Dirichlet Beta function derivative derived?

Can $\Gamma(1/5)$ be written in this form?