New posts in gamma-function

Show some properties of the Digamma Function

complex-analysis special-functions gamma-function polygamma

Is $\frac{1}{\pi}\int_{0}^{\infty} \Gamma(\sigma +xi)^2\,\Gamma(\sigma-xi)^2 \,dx = \frac{\Gamma(2\,\sigma)^4}{\Gamma(4\,\sigma)}$?

integration number-theory definite-integrals closed-form gamma-function

Proving and deriving a Gamma function

calculus real-analysis special-functions gamma-function

Great difficulty in finding the residues of $\frac{\mathrm{Log}\Gamma\left(\frac{z+ai}{2\pi i}\right)}{\cosh(z)+1}$

complex-analysis limits gamma-function residue-calculus polygamma

Definition of the gamma function for non-integer negative values

gamma-function

How prove this integral $ \int\limits_0^1 \int\limits_0^1 \ln\Gamma(x+y^3)\,dx\,dy =-\frac 7 {16}+\frac{1}{2}\ln 2\pi$

calculus integration multivariable-calculus definite-integrals gamma-function

References on binomial coefficients of the form $\binom{-1/m}{k} $

combinatorics reference-request binomial-coefficients gamma-function

The uniqueness of the Gamma Function

real-analysis special-functions gamma-function

What is the general formula of the sum $\sum_{k=0}^{n}(-1)^{k} \binom{n}{k}\binom{k/2}{m}$ for $m,n\in\mathbb{N}$?

combinatorics summation gamma-function polygamma combinatorial-number-theory

Is there a combinatorial way to see the link between the beta and gamma functions?

combinatorics special-functions binomial-coefficients gamma-function

Sum of $\Gamma(n+a) / \Gamma(n+b)$

calculus real-analysis sequences-and-series gamma-function

Closed form for an integral involving the incomplete Gamma function?

calculus integration complex-analysis fourier-transform gamma-function

How does one convert an integrand of the form $\frac{x\sinh x-t\sinh t}{\sinh^2x-\sinh^2t}$ into the form $\frac{\ln(x^2-t^2+1)}{\sinh^2x-\sinh^2t}$?

definite-integrals logarithms contour-integration gamma-function hyperbolic-functions

Seeking Methods to solve $\int_{0}^{\infty} \frac{e^{-x^n}}{x^n + 1}\:dx $

real-analysis integration definite-integrals gamma-function

Show that the Gamma integral exists for $x > 0$.

calculus gamma-function

Improper integral of $\log x \operatorname{sech} x$

integration complex-analysis improper-integrals gamma-function

Ramanujan's 'well known' integral, $\int\limits_{-\pi/2}^{\pi/2} (\cos x)^m e^{in x}dx$.

integration contour-integration gamma-function

Special Gamma function integral

integration definite-integrals special-functions gamma-function

What is this series relating to the residues of the Gamma function?

sequences-and-series special-functions gamma-function

Looking for a limit

limits probability-theory gamma-function binomial-distribution distribution-tails