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Schlömilch's Function

S(nu,z)=int_0^infty(1+t)^(-nu)e^(-zt)dt
(1)
=z^(nu-1)e^zint_z^inftyu^(-nu)e^(-u)du
(2)
=z^(nu/2-1)e^(z/2)W_(-nu/2,(1-nu)/2)(z),
(3)

where W_(k,m)(z) is the Whittaker function.

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Cite this as:

Weisstein, Eric W. "Schlömilch's Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SchloemilchsFunction.html

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