Double series expression for the Stieltjes constants

2010/07/31 by Coffey, Mark W.
#11M06 #11M35 #11Y60 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1008.0037

Abstract

We present expressions in terms of a double infinite series for the Stieltjes constants γ_k(a). These constants appear in the regular part of the Laurent expansion for the Hurwitz zeta function. We show that the case γ_k(1)=γ corresponds to a series representation for the Riemann zeta function given much earlier by Brun. As a byproduct, we obtain a parameterized double series representation of the Hurwitz zeta function.

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