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 Ik,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 Ik,n we offer formulas for the explicit values of Ramanujan’s cubic continued fraction and χ(eπn).

Keywords

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

AMS Classification

  • 33D90
  • 11F20

References

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Cite this paper

APA

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.

Chicago

Saikia, Nipen and Jubaraj Chetry. “New Theorems on Explicit Evaluation of a Parameter of Ramanujan’s χ(q) Function.” Notes on Number Theory and Discrete Mathematics 23, no. 1 (2017): 7-18.

MLA

Saikia, Nipen and Jubaraj Chetry. “New Theorems on Explicit Evaluation of a Parameter of Ramanujan’s χ(q) Function.” Notes on Number Theory and Discrete Mathematics 23.1 (2017): 7-18. Print.

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