Orthogonal Polynomials related to g-fractions with missing terms

2017/01/27 by Kiran Kumar Behera, Behera, Kiran Kumar, A. Swaminathan +1
Mathematics · #30B70 #33C47 #42C05 #Advanced Mathematical Identities #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1701.07996

openalex publication_date 2017/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 are 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.

Citations

• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle

Related

• Multiple orthogonal polynomials associated with branched continued fractions for ratios of hypergeometric series
• Multiple orthogonal polynomials with respect to Gauss' hypergeometric function
• Generalized orthogonality and continued fractions
• Continued fractions and orthogonal polynomials in several variables
• Additions to the formula lists in "Hypergeometric orthogonal polynomials and their q-analogues" by Koekoek, Lesky and Swarttouw