Work

Mellin Transform of Weierstrass Zeta Function and Integral Representations of Some Lambert Series

Year: 2025

Type: article

Abstract: We consider a series which combines two Dirichlet series constructed from the coefficients of a Laurent series and derive a general integral representation of the series as a Mellin transform. As an application, we obtain a family of Mellin integral identities involving the Weierstrass elliptic functions and some Lambert series. These identities are used to derive some of the properties of the Lambert series.

Source: Mathematics

DOI: 10.3390/math13040582

Author: Namhoon Kim

Institution: Hongik University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Hongik University