The fifth and seventh order mock theta functions

Andrews, George E.

doi:10.1090/S0002-9947-1986-0814916-2

The fifth and seventh order mock theta functions
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Trans. Amer. Math. Soc. 293 (1986), 113-134 Request permission

Abstract:

The theory of Bailey chains is extended to yield identities for Hecke type modular forms and related generalizations. The extended results allow us to produce Hecke type series for the fifth and seventh order mock theta functions. New results on the generating function for sums of three squares also follow, and a new proof that every integer is the sum of three triangular numbers is given.

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