Relations between RαRβ and Rm functions related to Jacobi’s triple-product identity and the family of theta-function identities

M. P. Chaudhary
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 1–11
DOI: 10.7546/nntdm.2021.27.2.1-11
Full paper (PDF, 207 Kb)

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Authors and affiliations

M. P. Chaudhary
Department of Mathematics, Netaji Subhas University of Technology
Sector 3, Dwarka, New Delhi 110078, India

Abstract

In this paper, the author establishes a set of three new theta-function identities involving RαRβ and Rm 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 answer a open question of Srivastava et al [33], and established relations in terms of RαRβ and Rm (for m = 1, 2, 3), and q-products identities. Finally, we choose to further emphasize upon some close connections with combinatorial partition-theoretic identities.

Keywords

  • Theta-function identities
  • Multivariable R-functions
  • Jacobi’s triple-product identity
  • Ramanujan’s theta functions
  • q-Product identities
  • Euler’s Pentagonal Number Theorem
  • Rogers–Ramanujan continued fraction
  • Rogers–Ramanujan identities
  • Combinatorial partition-theoretic identities

2020 Mathematics Subject Classification

  • 05A17
  • 05A30
  • 11F27
  • 11P83

References

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Cite this paper

Chaudhary, M. P. (2021). Relations between RαRβ and Rm functions related to Jacobi’s triple-product identity and the family of theta-function identities. Notes on Number Theory and Discrete Mathematics, 27(2), 1-11, DOI: 10.7546/nntdm.2021.27.2.1-11.

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