The tri-pentagonal number theorem and related identities

Details The tri-pentagonal number theorem and related identities The tri-pentagonal number theorem and related identities

2008-01-20

arxiv.org/abs/0801.3008v1

Mathematics

Number Theory

13 pages

Scientific paper

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.

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