Nu function

Template:Short description In mathematics, the nu function is a generalization of the reciprocal gamma function of the Laplace transform.

Formally, it can be defined as

$\begin{array}{cc}\nu (x)& \equiv {\int }_0^{\mathrm{\infty }}\frac{x^{t}dt}{\Gamma (t+1)}\\ \nu (x,\alpha )& \equiv {\int }_0^{\mathrm{\infty }}\frac{x^{\alpha +t}dt}{\Gamma (\alpha +t+1)}\end{array}$

where $\Gamma (z)$ is the Gamma function.