Special Functions

Abstract

Consider the semi-plane $\Delta _0=\{z\in C,\;z=x+iy:x>0\}$. The complex function $\Gamma :\Delta _0\rightarrow C$ defined by

$$ \Gamma (z)=\int \limits _{0}^{\infty }t^{z-1}e^{-t}\mathrm {d}t, $$

is called the Euler’s function of first species.