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)**

## Details

### 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 *R _{α}*,

*R*and

_{β}*R*functions which are based upon a number of

_{m}*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

*R*,

_{α}*R*and

_{β}*R*(for

_{m}*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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## Related papers

## Cite this paper

Chaudhary, M. P. (2021). Relations between *R _{α}*,

*R*and

_{β}*R*functions related to Jacobi’s triple-product identity and the family of theta-function identities.

_{m}*Notes on Number Theory and Discrete Mathematics*, 27(2), 1-11, DOI: 10.7546/nntdm.2021.27.2.1-11.