Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Download PDF
27 pages

Loading next page...
 
/lp/springer_journal/orthogonal-polynomials-related-to-g-g-fractions-with-missing-terms-SJbCueORjC
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 Theory – Springer Journals

Published: Oct 24, 2017

References

  • Special Functions, Encyclopedia of Mathematics and its Applications
    Andrews, GE; Askey, R; Roy, R
  • Mapping properties of basic hypergeometric functions
    Baricz, Á; Swaminathan, A
  • On perturbed Szegő recurrences
    Castillo, K
  • On co-polynomials on the real line
    Castillo, K; Marcellán, F; Rivero, J
  • The interpolation of pick functions
    Donoghue, WF
  • Univalent Functions, Grundlehren der Mathematischen Wissenschaften
    Duren, PL
  • Szegő transformations and rational spectral transformations for associated polynomials
    Garza, L; Marcellán, F
  • A generalization of starlike functions
    Ismail, MEH; Merkes, E; Styer, D
  • Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle
    Jones, WB; Njåstad, O; Thron, WJ
  • Continued Fractions, Encyclopedia of Mathematics and its Applications
    Jones, WB; Thron, WJ
  • Mapping properties of hypergeometric functions and convolutions of starlike or convex functions of order $$\alpha $$ α
    Küstner, R
  • On the order of starlikeness of the shifted Gauss hypergeometric function
    Küstner, R
  • Continued Fractions with Applications, Studies in Computational Mathematics, 3
    Lorentzen, L; Waadeland, H
  • On typically-real functions in a cut plane
    Merkes, EP
  • Convergence of the Schur algorithm
    Njåstad, O
  • Über Potenzreihen dei im Inneren des Einheitskreises beschränkt sind
    Schur, J
  • Ranga, Szegő polynomials from hypergeometric functions
    Sri, A
  • Orthogonal Polynomials
    Szegő, G
  • On the convergence of continued fractions at Runckel’s points
    Tsygvintsev, AV
  • Bounded analytic maps, Wall fractions and $$ABC$$ A B C -flow
    Tsygvintsev, A
  • Continued fractions and bounded analytic functions
    Wall, HS
  • Analytic Theory of Continued Fractions
    Wall, HS
  • Rational spectral transformations and orthogonal polynomials
    Zhedanov, A