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
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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

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