New posts in Hypergeometric Function

Is it true that $\int_0^1 \big(K(k^{1/2})\big)^2\,dk = \frac{7}2\zeta(3)$?

How to calculate the Kampé de Fériet function?

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

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

About the integral $\int_{0}^{\pi/4}\log^4(\cos\theta)\,d\theta$

The integral of an elliptic integral: $\int_{0}^{1}\frac{x\mathbf{K}^2\left ( x \right )}{\sqrt{1-x^{2}}}\mathrm{d}x$

Why does $\sum\limits_{i=0}^{100} \binom{100}{i} \sum\limits_{j=i+1}^{101}\binom{101}{j}$ equal $2^{200}$?

Help needed finding a closed form or approximation for an integral(hypergeometric function)

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

Computing the Integral $\int\tanh[b(x-a)]\cos\beta x\,dx$