A q-CONTINUED FRACTION-Reference-Cited by-同舟云学术

A q-CONTINUED FRACTION

Published:2006-12 Issue:04 Volume:02 Page:523-547
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BOWMAN D.¹,Mc LAUGHLIN J.²,WYSHINSKI N. J.³

Affiliation:

1. Northern Illinois University, Mathematical Sciences, DeKalb, IL 60115-2888, USA

2. Mathematics Department, Anderson Hall, West Chester University, West Chester, PA 19383, USA

3. Mathematics Department, Trinity College, 300 Summit Street, Hartford, CT 06106-3100, USA

Abstract

We use the method of generating functions to find the limit of a q-continued fraction, with 4 parameters, as a ratio of certain q-series. We then use this result to give new proofs of several known continued fraction identities, including Ramanujan's continued fraction expansions for (q2; q3)∞/(q; q3)∞and [Formula: see text]. In addition, we give a new proof of the famous Rogers–Ramanujan identities. We also use our main result to derive two generalizations of another continued fraction due to Ramanujan.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304210600070X

Reference22 articles.

1. ON q-DIFFERENCE EQUATIONS FOR CERTAIN WELL-POISED BASIC HYPERGEOMETRIC SERIES

2. Two theorems of Gauss and allied identities proved arithmetically

3. G. E. Andrews, Combinatorics and Ramanujan's "Lost" Notebook, London Math. Soc. Lecture Note Series 103 (Cambridge University Press, London, 1985) pp. 1–23.

4. G. E. Andrews and B. C. Berndt, Ramanujan's Lost Notebook, Part I (Springer, New York, 2005) p. xiv + 437.

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1. Orthogonal polynomials associated with a continued fraction of Hirschhorn;The Ramanujan Journal;2022-01-24

2. Applications of the Heine and Bauer–Muir transformations to Rogers–Ramanujan type continued fractions;Journal of Mathematical Analysis and Applications;2017-03

3. On some continued fraction expansions of the Rogers–Ramanujan type;The Ramanujan Journal;2011-10-28

4. Continued fraction proofs of m-versions of some identities of Rogers–Ramanujan–Slater type;The Ramanujan Journal;2011-03-10

5. On Diophantine approximations of Ramanujan type q-continued fractions;Journal of Number Theory;2009-05