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Periodic Zeta Function

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A periodic zeta function is defined by

F(x,s)=sum_(m=1)^(infty)(e^(2piimx))/(m^s)
(1)
=psi_s(e^(2piix)),
(2)

where psi_s(x) is the polygamma function.

See also

Polygamma Function, Riemann Zeta Function, Zeta Function

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References

Apostol, T. M. Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, p. 55, 1997.

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Periodic Zeta Function

Cite this as:

Weisstein, Eric W. "Periodic Zeta Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PeriodicZetaFunction.html

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