New posts in Beta Function

Show that $\sum_{n=0}^{\infty}\frac{2^n(5n^5+5n^4+5n^3+5n^2-9n+9)}{(2n+1)(2n+2)(2n+3){2n\choose n}}=\frac{9\pi^2}{8}$

How could one solve $\int_{0}^{\infty} \frac{1}{1-t^4}dt$ with special functions?

Relation between Beta and Gamma functions