Power series expansions of Riemann’s 𝜉 function

Keiper, J. B.

doi:10.1090/S0025-5718-1992-1122072-5

Power series expansions of Riemann’s $\xi$ function
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Math. Comp. 58 (1992), 765-773 Request permission

Abstract:

We show how high-precision values of the coefficients of power series expansions of functions related to Riemann’s $\xi$, 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^extsctm.

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