Rank-Crank type PDE's for higher level Appell functions

2009/08/27 by Sander Zwegers, Zwegers, Sander · 1 citation
Mathematics · #11F11 #11F27 #11F50 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0908.4007

openalex publication_date 2009/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider level l Appell functions, and find a partial differential equation for all odd l. For l=3 this recovers the Rank-Crank PDE, found by Atkin and Garvan, and for l=5 we get a similar PDE found by Garvan.

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