Recurrence relations connecting mock theta functions and restricted partition functions

M. Rana, H. Kaur and K. Garg
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 2, Pages 360–371
DOI: 10.7546/nntdm.2023.29.2.360-371
Full paper (PDF, 234 Kb)

Details

Authors and affiliations

M. Rana
School of Mathematics, Thapar Institute of Engineering and Technology
Patiala-147004, Punjab, India

H. Kaur
School of Mathematics, Thapar Institute of Engineering and Technology
Patiala-147004, Punjab, India

K. Garg
School of Mathematics, Thapar Institute of Engineering and Technology
Patiala-147004, Punjab, India

Abstract

In this paper, we provide some recurrence relations connecting restricted partition functions and mock theta functions. Elementary manipulations are used including Jacobi triple product identity, Euler’s pentagonal number theorem, and Ramanujan’s theta functions for finding the recurrence relations.

Keywords

• Partition
• Generating function
• Recurrence relation
• Mock theta function

2020 Mathematics Subject Classification

• 05A15
• 05A17
• 05A30
• 11A67
• 11B37
• 11P81

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Manuscript history

• Received: 30 September 2022
• Revised: 4 April 2023
• Accepted: 12 May 2023
• Online First: 16 May 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).