New proofs for three identities of seventh order mock theta functions

Abstract

Using the three-term Weierstrass relation for theta functions and the properties of Hecke-type double sums and Appell-Lerch sums, we give new and simple proofs for the seventh order mock theta conjectures.

Keywords

• mock theta functions
• hecke-type double sums
• appell-lerch sums
• the three-term weierstrass relation