4
votes
1answer
412 views

Is there a closed form expression/series expansion for $\int_{\epsilon-i\infty}^{\epsilon+i\infty} e^{az+b^2z^2}\Gamma(z)\Gamma(1-z)dz$ ?

I've been trying to find a closed form expression/series expansion for the following integral without success: $$F(a,b)=\int_{\epsilon-i\infty}^{\epsilon+i\infty} ...
1
vote
0answers
481 views

Derivative of the regularized upper incomplete gamma function

Hello everyone! I have a question about the derivative of the regularized upper incomplete gamma function. Considering the gamma function and the incomplete gamma function \begin{eqnarray} ...
5
votes
1answer
222 views

On the multidimensional generalisation of Gamma function

Gamma function is defined as $$ \Gamma(z) = \int\limits_{0}^{+\infty} x^{z-1} e^{-x} \; dx $$ I'm looking for multidimensional generalisation of this definition. I consider the class $Q$ of ...