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

Namhoon Kim ()
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Namhoon Kim: Department of Mathematics Education, Hongik University, 94 Wausan-ro, Mapo-gu, Seoul 04066, Republic of Korea

Mathematics, 2025, vol. 13, issue 4, 1-14

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.

Keywords: Mellin transform; Weierstrass zeta function; Lambert series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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