English

The tri-pentagonal number theorem and related identities

Number Theory 2008-01-22 v1 Combinatorics

Abstract

I revisit an automated proof of Andrews' pentagonal number theorem found by Riese. I uncover a simple polynomial identity hidden behind his proof. I explain how to use this identity to prove Andrews' result along with a variety of new formulas of similar type. I reveal an interesting relation between the tri-pentagonal theorem and items (19), (20), (94), (98) on the celebrated Slater list. Finally, I establish a new infinite family of multiple series identities.

Keywords

Cite

@article{arxiv.0801.3008,
  title  = {The tri-pentagonal number theorem and related identities},
  author = {Alexander Berkovich},
  journal= {arXiv preprint arXiv:0801.3008},
  year   = {2008}
}

Comments

13 pages

R2 v1 2026-06-21T10:04:31.356Z