The last of the hypergeometric continued fractions
Classical Analysis and ODEs
2016-09-06 v1
Abstract
A contiguous relation for complementry pairs of very well poised balanced basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. This generalizes the continued fraction results associated with both Ramanujan's Entry 40 and Askey-Wilson polynomials which can be recovered as limits. Associated with our continued fraction results there are systems of biorthogonal rational functions that have yet to be derived.
Keywords
Cite
@article{arxiv.math/9409229,
title = {The last of the hypergeometric continued fractions},
author = {David R. Masson},
journal= {arXiv preprint arXiv:math/9409229},
year = {2016}
}