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A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity

Author

Listed:
  • Hari Mohan Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan)

  • Rekha Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada)

  • Mahendra Pal Chaudhary

    (Department of Mathematics, Netaji Subhas University of Technology, Sector 3, Dwarka, New Delhi 110078, India)

  • Salah Uddin

    (Department of Mathematics, PDM University, Bahadurgarh 124507, Haryana State, India)

Abstract

The authors establish a set of six new theta-function identities involving multivariable R -functions which are based upon a number of q -product identities and Jacobi’s celebrated triple-product identity. These theta-function identities depict the inter-relationships that exist among theta-function identities and combinatorial partition-theoretic identities. Here, in this paper, we consider and relate the multivariable R -functions to several interesting q -identities such as (for example) a number of q -product identities and Jacobi’s celebrated triple-product identity. Various recent developments on the subject-matter of this article as well as some of its potential application areas are also briefly indicated. Finally, we choose to further emphasize upon some close connections with combinatorial partition-theoretic identities and present a presumably open problem.

Suggested Citation

  • Hari Mohan Srivastava & Rekha Srivastava & Mahendra Pal Chaudhary & Salah Uddin, 2020. "A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity," Mathematics, MDPI, vol. 8(6), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:918-:d:367606
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