Double series expression for the Stieltjes constants

Details Double series expression for the Stieltjes constants Double series expression for the Stieltjes constants

2010-07-31

arxiv.org/abs/1008.0037v2

Physics

Mathematical Physics

12 pages, no figures, updated and typos corrected; to appear in Analysis

Scientific paper

We present expressions in terms of a double infinite series for the Stieltjes constants $\gamma_k(a)$. These constants appear in the regular part of the Laurent expansion for the Hurwitz zeta function. We show that the case $\gamma_k(1)=\gamma$ 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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