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Mu Function

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

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

See also Lambda Function, Nu 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