Nu function

In mathematics, the nu function is a generalization of the reciprocal gamma function of the Laplace transform.

Formally, it can be defined as



\begin{align} \nu(x) & \equiv \int_0^\infty \frac{x^t \, dt}{\Gamma(t+1)} \\[10pt] \nu(x,\alpha) & \equiv \int_0^\infty \frac{x^{\alpha+t} \, dt}{\Gamma(\alpha+t+1)} \end{align} $$

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