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.
"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