New modular relations for the Rogers–Ramanujan type functions of order fifteen

Chandrashekar Adiga and A. Vanitha
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 1, Pages 36–48
Full paper (PDF, 195 Kb)

Details

Authors and affiliations

Chandrashekar Adiga
Department of Studies in Mathematics
University of Mysore
Manasagangotri, Mysore 570 006, India

A. Vanitha
Department of Studies in Mathematics
University of Mysore
Manasagangotri, Mysore 570 006, India

Abstract

In this paper, we establish two modular relations for the Rogers–Ramanujan–Slater functions of order fifteen. These relations are analogues to Ramanujan’s famous forty identities for the Rogers–Ramanujan functions.
Furthermore, we give interesting partition theoretic interpretations of these relations.

Keywords

• Rogers–Ramanujan functions
• Theta functions
• Jacobi’s triple product identity
• Colored partitions

AMS Classification

• 33D15
• 11P83

References

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