A Study of Generalized Partial Mock Theta Functions

Abstract

. S. Ramanujan in his last letter to G.H. Hardy has introduced sev-enteen mock theta functions of di  erenct orders ( 3,5 and 7) without explicitly mentioning the reason for his levelling of order, later Watson added to this set three more third order mock theta function. Watson also de  ned bilateral form of some mock theta function of order  ve and expressed them in terms of lerch transendetal functions . Patial mock theta functions of sixth order were studied by Y.S. Choi and partial mock theta functions of third order were studied by G.E. Andrews. In this paper we have given generalization of partial sixth and third order mock theta functions and it is shown that these generalized partial mock theta functions are F q functions. q-integral representation of these generalized partial mock theta functions are also given. we have also expressed some bilateral mock theta functions in terms of lerch transcendental functions f ( x, ξ ; q,p ).