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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## Details

### 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*we offer formulas for the explicit values of Ramanujan’s cubic continued fraction and

_{k,n}*χ*(e

^{−πn}).

### Keywords

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

### AMS Classification

- 33D90
- 11F20

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## Cite this paper

Saikia, N., & Chetry, J. (2017). New theorems on explicit evaluation of a parameter of Ramanujan’s *χ*(*q*) function. Notes on Number Theory and Discrete Mathematics, 23(1), 7-18.