New theorems on explicit evaluation of a parameter of Ramanujan’s χ(q) function

Nipen Saikia and Jubaraj Chetry
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 1, Pages 7–18
Full paper (PDF, 184 Kb)

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Authors and affiliations

Nipen Saikia 
Department of Mathematics, Rajiv Gandhi University
Rono Hills, Doimukh-791112, Arunachal Pradesh, India

Jubaraj Chetry 
Department of Mathematics, Rajiv Gandhi University
Rono Hills, Doimukh-791112, Arunachal Pradesh, India

Abstract

We prove many new theorems for the explicit values of the parameter I_k,n, for positive real number n and k, involving Ramanujan’s χ(q) function by establishing its connection with some other parameters of Ramanujan’s theta-functions. As applications of the parameter I_k,n we offer formulas for the explicit values of Ramanujan’s cubic continued fraction and χ(e^−πn).

Keywords

• Ramanujan’s theta-function
• Parameters
• Explicit values
• Ramanujan’s cubic continued fraction

AMS Classification

• 33D90
• 11F20

References

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