On a series of Ramanujan, dilogarithm values, and solitons

Boyadzhiev, Khristo N.; Manns, Steven

doi:10.2140/involve.2022.15.411

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On a series of Ramanujan, dilogarithm values, and solitons

Khristo N. Boyadzhiev and Steven Manns

Vol. 15 (2022), No. 3, 411–425

DOI: 10.2140/involve.2022.15.411

Abstract

We discuss several topics related to polylogarithms with a focus on dilogarithms. The topics are a generating function with harmonic numbers coming from Ramanujan, extending the dilogarithm to complex numbers beyond the unit disk, and relating polylogarithms to Bernoulli polynomials and to solitons. Several improvements and corrections are made to existing representations.

Keywords

harmonic number, generating function, dilogarithm, trilogarithm, polylogarithm, Bernoulli polynomial, Riemann zeta function, solitons

Mathematical Subject Classification

Primary: 11M41, 33B30

Milestones

Received: 5 April 2021

Revised: 23 November 2021

Accepted: 27 November 2021

Published: 2 December 2022

Communicated by H. M. Srivastava

Authors

Khristo N. Boyadzhiev
Department of Mathematics Ohio Northern University Ada, OH United States

Steven Manns
Department of Mathematics Ohio Northern University Ada, OH United States

Vol. 15, No. 3, 2022