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

$\begin{array}{rl}\nu (x)& \equiv \underset{0}{\overset{\mathrm{\infty }}{\int }}\frac{x^{t}dt}{\mathrm{\Gamma }(t+1)}\\ \nu (x,\alpha )& \equiv \underset{0}{\overset{\mathrm{\infty }}{\int }}\frac{x^{\alpha +t}dt}{\mathrm{\Gamma }(\alpha +t+1)}\end{array}$

where $\mathrm{\Gamma }(z)$ is the Gamma function.

See also

• Lambda function (disambiguation)
• Mu function

External links

• Weisstein, Eric W.. "Nu function". http://mathworld.wolfram.com/NuFunction.html.