February 2022 A series representation of Euler–Stieltjes constants and an identity of Ramanujan
Tapas Chatterjee, Suraj Singh Khurana
Rocky Mountain J. Math. 52(1): 49-64 (February 2022). DOI: 10.1216/rmj.2022.52.49


We derive a series representation of the generalized Stieltjes constants which arise in the Laurent series expansion of partial zeta function at the point s=1. 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 k-th derivative of Dirichlet series with periodic coefficients at the point s=1. Another application involves evaluation of a class of infinite products of which a special case is an identity of Ramanujan.


Download 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


Received: 21 January 2021; Revised: 22 May 2021; Accepted: 24 May 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

MathSciNet: MR4409916
zbMATH: 1498.11172
Digital Object Identifier: 10.1216/rmj.2022.52.49

Primary: 11M06 , 30B50 , 30D05
Secondary: 11Y60 , 33B15

Keywords: Dirichlet L-series , functional equation , Gamma function , generalized Euler constants , Weierstrass product formula

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium


This article is only available to subscribers.
It is not available for individual sale.

Vol.52 • No. 1 • February 2022
Back to Top