Nu Function

$\displaystyle \nu(x)$	$\textstyle \equiv$	$\displaystyle \int_0^\infty {x^t\,dt\over \Gamma(t+1)}$
$\displaystyle \nu(x,\alpha)$	$\textstyle \equiv$	$\displaystyle \int_0^\infty {x^{\alpha+t}\,dt\over \Gamma(\alpha+t+1)},$

where $\Gamma(z)$ is the Gamma Function. See Gradshteyn and Ryzhik (1980, p. 1079).

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, 1979.