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Some New General Theorems for the Explicit Evaluations of the Rogers–Ramanujan Continued Fraction

Some New General Theorems for the Explicit Evaluations of the Rogers–Ramanujan Continued Fraction We prove several new general theorems for the explicit evaluation of the Rogers–Ramanujan continued fraction $$R(q)$$ R ( q ) by parametrization of Ramanujan’s theta-functions and give examples. We also establish general theorems for the explicit evaluation of the parameter $$k:=R(q)R^2(q)$$ k : = R ( q ) R 2 ( q ) defined by Ramanujan in his notebook leading to the explicit evaluations of $$R(q)$$ R ( q ) . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Some New General Theorems for the Explicit Evaluations of the Rogers–Ramanujan Continued Fraction

Computational Methods and Function Theory , Volume 13 (4) – Oct 22, 2013

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-013-0040-0
Publisher site
See Article on Publisher Site

Abstract

We prove several new general theorems for the explicit evaluation of the Rogers–Ramanujan continued fraction $$R(q)$$ R ( q ) by parametrization of Ramanujan’s theta-functions and give examples. We also establish general theorems for the explicit evaluation of the parameter $$k:=R(q)R^2(q)$$ k : = R ( q ) R 2 ( q ) defined by Ramanujan in his notebook leading to the explicit evaluations of $$R(q)$$ R ( q ) .

Journal

Computational Methods and Function TheorySpringer Journals

Published: Oct 22, 2013

References