New posts in Gamma Function

Evaluating $I(z,s)=\int_0^1\int_0^1\left(1-\frac{(1-x)(1-y)}{(1-(1-z)x)(1-(1-z)y)}\right)^{s-2}\,\mathrm dx\mathrm dy$

Asymptotic behavior of a Fourier/Laplace transform

Prove that $_4F_3\left(\frac13,\frac13,\frac23,\frac23;1,\frac43,\frac43;1\right)=\frac{\Gamma \left(\frac13\right)^6}{36 \pi ^2}$

Show $\binom{n}{[n/2]} = \binom{n-1}{[(n-1)/2]} + \sum_{i=0}^{[n/2] - 1} \frac{1}{i+1} \binom{2i}{i} \binom{n-2i-2}{[n/2]- i - 1}$

Proving $\int_0^\infty\left(\frac{x^xe^{-x}}{\Gamma(x+1)}-\frac1{\sqrt{2\pi x}}\right)dx=-\frac13$

Prove that $f(x_0)>\frac{2}{3}$

Evalute triple sum $ \sum_{m\geq 0}\sum_{n \geq 0}\sum_{p\geq 0} \frac{m!n!p!}{(m+n+p+2)!}$

Proving $\sum_{n=0}^\infty\frac{(-1)^n\Gamma(2n+a+1)}{\Gamma(2n+2)}=2^{-a/2}\Gamma(a)\sin(\frac{\pi}{4}a)$

Alternative approaches to showing that $\Gamma'(1/2)=-\sqrt\pi\left(\gamma+\log(4)\right)$

How to evaluate $\int_{0}^{1} \! \frac{-\ln(1-t)}{t} \, \mathrm{d}t$ without using taylor series expansion?