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Orthogonal Polynomials Related to $$_{g}$$ g -Fractions with Missing Terms

Orthogonal Polynomials Related to $$_{g}$$ g -Fractions with Missing Terms The purpose of the present paper is to investigate some structural and qualitative aspects of two different perturbations of the parameters of g-fractions. In this context, the concept of gap g-fractions is introduced. While tail sequences of a continued fraction play a significant role in the first perturbation, Schur fractions are used in the second perturbation of the g-parameters that is considered. Illustrations are provided using Gaussian hypergeometric functions. Using a particular gap g-fraction, some members of the class of Pick functions are also identified. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Orthogonal Polynomials Related to $$_{g}$$ g -Fractions with Missing Terms

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-017-0218-y
Publisher site
See Article on Publisher Site

Abstract

The purpose of the present paper is to investigate some structural and qualitative aspects of two different perturbations of the parameters of g-fractions. In this context, the concept of gap g-fractions is introduced. While tail sequences of a continued fraction play a significant role in the first perturbation, Schur fractions are used in the second perturbation of the g-parameters that is considered. Illustrations are provided using Gaussian hypergeometric functions. Using a particular gap g-fraction, some members of the class of Pick functions are also identified.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Oct 24, 2017

References