Some new mock theta functions

Abstract

Mock theta functions can be represented by Eulerian forms, Hecke-type double sums, Appell–Lerch sums, and Fourier coefficients of meromorphic Jacobi forms. In view of some q-series identities, we establish three two-parameter mock theta functions, and express them in terms of Appell-Lerch sums. In addition, we find three mock theta functions in Eulerian forms. Then in light of their Hecke-type double sums, we provide the Hecke-type double sums for some third order mock theta functions, and establish the relations between these functions and some classical mock theta functions.