New posts in Special Functions

Proving $\sum _{k=1}^n \frac{(-1)^{k-1} 16^k (k-1)! k! (k+n-1)!}{((2 k)!)^2 (n-k)!}=\frac{4}{n}\sum _{k=1}^n \frac{1}{2 k-1}$

Show: $\int_0^1\int_0^1\frac{dx\,dt}{(xt)^2+xt+1}=\frac{2}{\sqrt3}\mathrm{Cl}_2\left(\tfrac{2\pi}{3}\right)$

What even *are* elliptic functions?

Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$

Proving $\int_{\sqrt{\frac{3}{5}}}^1 \frac{\arctan (x)}{\sqrt{2 x^2-1} \left(3 x^2-1\right)} \, dx=\frac{3 \pi ^2}{160}$

Integral involving hypergeometric function $\int_0^1[{}_2F_1(\frac13,\frac23;1;x^3)]^2dx$

Examining $\int_0^1 \left(\frac{x - 1}{\ln(x)} \right)^n\:dx$

closed formula for: $(g\partial)^n$

The Apéry's constant and the Airy function

Closed form for $f(x)=\ _3F_2\left(\tfrac12,\tfrac12,\tfrac12;\tfrac32,\tfrac32;x\right)$