Abstract
We derive a series representation of the generalized Stieltjes constants which arise in the Laurent series expansion of partial zeta function at the point . In the process, we introduce a generalized gamma function and deduce its properties such as functional equation, Weierstrass product and reflection formulas along the lines of the study of a generalized gamma function introduced by Dilcher in 1994. These properties are used to obtain a series representation for the -th derivative of Dirichlet series with periodic coefficients at the point . Another application involves evaluation of a class of infinite products of which a special case is an identity of Ramanujan.
Citation
Tapas Chatterjee. Suraj Singh Khurana. "A series representation of Euler–Stieltjes constants and an identity of Ramanujan." Rocky Mountain J. Math. 52 (1) 49 - 64, February 2022. https://doi.org/10.1216/rmj.2022.52.49
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