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Power Series Expansions of Riemann's Zeta Function

Jerry B. Keiper
Organization: Wolfram Research, Inc.
Journal / Anthology

Mathematics of Computation
Year: 1992
Volume: 58
Page range: 765-773

We show how high-precision values of the coefficients of power series expansions of functions related to Riemann's Zeta function may be calculated. We also show how the Stieltjes constants can be evaluated using this scheme and how the Riemann hypothesis can be expressed in terms of the behavior of two of the sequences of coefficients. High-precision values for the coefficients of these power series are found using Mathematica.

*Mathematics > Calculus and Analysis > Series
*Mathematics > Calculus and Analysis > Special Functions