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New fifth and seventh order mock theta function identities

arXiv:1907.04803

Abstract

We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan fifth order mock theta functions $χ_0(q)$ and $χ_1(q)$ and all three of Ramanujan's seventh order mock theta functions. We find that the coefficients of the three mock theta functions of order 7 are surprisingly related.

16 pages, accepted to appear in the GEA80 Special Issue of the Annals of Combinatorics