
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.
Mathematics - Number Theory, FOS: Mathematics, Mathematics - Combinatorics, 33D15, 11B65, Number Theory (math.NT), Combinatorics (math.CO)
Mathematics - Number Theory, FOS: Mathematics, Mathematics - Combinatorics, 33D15, 11B65, Number Theory (math.NT), Combinatorics (math.CO)
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