Article ID: MTJPAM-D-21-00075

Title: Bilateral mock theta functions of order eleven and their Lerch representations


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00075; Volume 4 / Issue 2 / Year 2022, Pages 60-71

Document Type: Research Paper

Author(s): Mohammad Ahmad a , Shahab Faruqi b

aDepartment of Mathematics, National Defence Academy, Khadakwasla, Pune, India

bDepartment of Mathematics, National Defence Academy, Khadakwasla, Pune, India

Received: 14 December 2021, Accepted: 1 June 2022, Published: 10 August 2022.

Corresponding Author: Mohammad Ahmad (Email address: mahmad_786@rediffmail.com)

Full Text: PDF


Abstract

We use bilateral basic hypergeometric series to obtain some bilateral mock theta functions and show that these functions are related to the basic hypergeometric series 6Φ5. Also Ramanujan’s characterization of mock theta functions is satisfied by these functions. We also express them in terms of the Lerch’s transcendental function f(x, ξ; q, p).

Keywords: Mock theta functions, bilateral mock theta functions, Lerch transcendent, hypergeometric series, characteristic property, unit circle

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