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Psi Function

\Psi(z,s,v)\equiv \sum_{n=0}^\infty {z^n\over (v+n)^s}

for $\vert z\vert<1$ and $v\not = 0, -1$, ... (Gradshteyn and Ryzhik 1980, pp. 1075-1076).

See also Hurwitz Zeta Function, Ramanujan Psi Sum, Theta 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