New posts in gamma-function

Interesting Integral $\int_{-\infty}^{\infty}\frac{e^{i nx}}{\Gamma(\alpha+x) \Gamma(\beta -x)}dx$

integration special-functions improper-integrals gamma-function

Quotient of gamma functions?

special-functions gamma-function

Is $K\left(\frac{\sqrt{2-\sqrt3}}2\right)\stackrel?=\frac{\Gamma\left(\frac16\right)\Gamma\left(\frac13\right)}{4\ \sqrt[4]3\ \sqrt\pi}$

calculus special-functions gamma-function closed-form conjectures

Continuous generalization of $\sum_{k=0}^n {n \choose k} = 2^n$?

special-functions binomial-coefficients gamma-function

Find closed form of $f(x)= \frac{1}{x} \sum_{i=1}^{k} f(x+i)$

functional-equations gamma-function

Evaluating $\lim_{n\to\infty}\frac{1}{n+1}(\omega+\nu)^{(n+1)}z^\nu{_2F_1}(1,\omega+\nu+1;n+2;1-z)$

sequences-and-series gamma-function hypergeometric-function zeta-functions stirling-numbers

Prove $\int_{0}^\infty \frac{1}{\Gamma(x)}\, \mathrm{d}x = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, \mathrm{d}x$

calculus definite-integrals gamma-function

Understanding a particular evaluation of $\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right)$

limits gamma-function infinite-product

Algorithm to compute Gamma function

algorithms numerical-methods special-functions gamma-function

What is the exact value of $\eta(6i)$?

special-functions gamma-function modular-forms

Integral that arises from the derivation of Kummer's Fourier expansion of $\ln{\Gamma(x)}$

integration special-functions fourier-series gamma-function

Closed form for $\sum_{n=1}^\infty\frac{(-1)^n n^4 H_n}{2^n}$

sequences-and-series summation gamma-function closed-form

How to come up with the gamma function?

special-functions intuition gamma-function

How to prove $\int_0^\infty J_\nu(x)^3dx\stackrel?=\frac{\Gamma(1/6)\ \Gamma(1/6+\nu/2)}{2^{5/3}\ 3^{1/2}\ \pi^{3/2}\ \Gamma(5/6+\nu/2)}$?

special-functions gamma-function closed-form conjectures hypergeometric-function

How to evaluate the limit of multifactorial $\lim_{n\to 0} \sqrt[n]{n!!!!\cdots !}$

real-analysis sequences-and-series limits factorial gamma-function

Real and imaginary part of Gamma function

special-functions gamma-function riemann-zeta

Did I derive a new form of the gamma function?

calculus reference-request recreational-mathematics factorial gamma-function

Is there any meaning to this "Super Derivative" operation I invented?

derivatives gamma-function bessel-functions fractional-calculus

Closed form for $\sum_{n=1}^\infty\frac{\psi(n+\frac{5}{4})}{(1+2n)(1+4n)^2}$

sequences-and-series special-functions gamma-function closed-form combinatorics

Closed form for $\int_0^\infty\left(\int_0^1\frac1{\sqrt{1-y^2}\sqrt{1+x^2\,y^2}}\mathrm dy\right)^3\mathrm dx.$

special-functions definite-integrals gamma-function closed-form hypergeometric-function