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.
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