A Study of Generalized Partial Mock Theta Functions

Document Type : Regular research papers

Authors

1 Department of Mathematics and Statistics,Faculty of Science, Integral University, Lucknow-226026, India

2 Department of Mathematics and Statistics, Faculty of Science, Integral University, Lucknow-226026, India

3 Dept of Mathematics, NDA Khadakwasla Pune -411023 , INDIA

Abstract

S. Ramanujan in his last letter to G.H. Hardy has introduced seventeen mock theta functions of differenct orders ( 3,5 and 7) without explicitly mentioning the reason for his levelling of order, later Watson addeded to this set three more third order mock theta function. Watson also defined bilateral form of some mock theta function of order five 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 Fq 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).

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History

  • Receive Date: 27 November 2023
  • Accept Date: 18 March 2024

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