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}
}
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13 pages