A Study of Generalized Partial Mock Theta Functions | ||||
| Electronic Journal of Mathematical Analysis and Applications | ||||
| Volume 12, Issue 2, 2024, Page 1-11 PDF (225.35 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/ejmaa.2024.251590.1096 | ||||
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| Authors | ||||
Swayam Tiwari1; sameena saba2; MOHAMMAD AHMAD  3
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| 1Department of Mathematics and Statistics,Faculty of Science, Integral University, Lucknow-226026, India | ||||
| 2Department of Mathematics and Statistics, Faculty of Science, Integral University, Lucknow-226026, India | ||||
| 3Dept 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). | ||||
| Keywords | ||||
| Basic hypergeometric series; partial mock theta functions; q-integral; Lerch transcendental function | ||||
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