New posts in Special Functions

Computing the integral $\displaystyle I=\int_{0}^{1}\sqrt{1-x^{\pi}}dx$

General formula for $\int^1_0 x^\alpha \log(1-x)\operatorname{Li}_2 (x)\, \mathrm dx$

For what $a$ and $b$ are there explicit expressions for $I(a, b) =\int_0^1 \int_0^1 \dfrac{dx\,dy}{1-x^ay^b} $?

Deriving exponential generating function for central trinomial coefficients

Is $\sum_{n\ge0}(-1)^n\frac{\Gamma(\tfrac{n+1}{2})}{\Gamma(\tfrac{n}2+1)}=\frac{2}{\sqrt{\pi}}$ true?

Prove $\int_0^1 \frac{dx}{(x-2) \sqrt[5]{x^2{(1-x)}^3}} = -\frac{2^{\frac{11}{10}} \pi}{\sqrt{5+\sqrt{5}}}$

Solving quintic equations of the form $x^5-x+A=0$

Derive the recurrence relations

Proving a closed form for an integral with nested radicals

Prove that $\sum _{k=1}^{n-1} \binom{n-1}{k} k^{k-1} (n-k)^{n-k-1}=n^{n-1}-n^{n-2}$