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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
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