Some identities of certain basic hypergeometric series and their applications to mock theta functions

摘要

Abstract In this paper, we first obtain the corresponding transformation formulas of the basic bilateral hypergeometric series involving universal mock theta functions. Meanwhile, some identities of bilateral series associated with classical mock theta functions are deduced. From the duals of second type for universal mock theta functions, two new Hecke-type identities are derived. Some special cases for classical mock theta functions are also obtained immediately. Finally, an identity for K2(x,q)documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$K_2(x,q)$$end{document} is discussed by a transformation formula.