English

A Dilogarithm Series and a Generalization of a Theorem of Bridgeman

Number Theory 2025-08-07 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.2410.21619,
  title  = {A Dilogarithm Series and a Generalization of a Theorem of Bridgeman},
  author = {Chance Sanford},
  journal= {arXiv preprint arXiv:2410.21619},
  year   = {2025}
}

Comments

Appeared in Integers vol. 25