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Thursday, March 9, 2017

**Abstract:** In his last letter to Hardy, Ramanujan defined ten mock theta functions of order 5 and three of order 7. He stated that the three mock theta functions of order 7 are not related. We give simple proofs of new Hecke double sum identities for two of the order 5 functions and all three of the order 7 functions. We find that the coefficients of Ramanujan's three mock theta functions of order 7 are surprisingly related.