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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).

See also Lambda Function, Mu Function


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

© 1996-9 Eric W. Weisstein