A Dilogarithm Series and a Generalization of a Theorem of Bridgeman

2024/10/28 by Chance Sanford, Sanford, Chance
Mathematics · #33B30 (Primary) 11B39 (Secondary) #Advanced Mathematical Theories #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2410.21619

openalex publication_date 2024/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using Abel's five-term relation, we derive a new two-parameter series identity for the Rogers dilogarithm. By specializing this identity, we obtain dilogarithm series involving Lucas sequences. These results generalize certain series identities of Bridgeman related to solutions of Pell's equations, which were obtained via a completely different approach.

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