New posts in Special Functions

Can we find the asymptotic behavior of this $f(x) =\int_{0}^{\infty}\frac{u^2}{1+\frac{e^{u^2}}{x}}du$?

An interesting identity involving Jacobi $\theta_4$ and $\zeta(2)$

Prove series form of fractional harmonic numbers

Integral $\int_{-1}^{1} \frac{1}{(1+u^2)^{n/2}} \exp{\left(-2\pi \frac{a^2+b^2}{1+u^2}\right)} \exp{\left(-4\pi i ab \frac{u}{1+u^2}\right)} du $

The Gudermannian function and Apéry's constant

About the integral $\int_{0}^{+\infty}\frac{\text{arcsinh}(x)\,\text{arcsinh}(\lambda x)}{x^2}\,dx$

A very odd-looking statement about $\zeta(3)$ and $\text{Li}_2\left(\frac{1}{\varphi^2}\right)$

On the closed form of a integral related to $cosh(x)$

$\sum_{n=1}^{\infty}(-1)^{n-1}\left({\beta(n)\over n}-\ln{n+1\over n}\right)=\ln\sqrt{2\over \pi}\cdot{2\over \Gamma^2\left({3\over 4}\right)}?$

How good is this approximation of $n$ factorial?