Orthogonal Polynomials Associated with Complementary Chain Sequences

Symmetry Integrability and Geometry-Methods and Applications

article

Kiran Kumar Behera¹  A. Sri Ranga²  A. Swaminathan¹ 

[1] Department of Mathematics, Indian Institute of Technology Roorkee;Departamento de Matemática Aplicada, IBILCE, UNESP-Univ.

关键词: chain sequences;    orthogonal polynomials;    recurrence relation;    Verblunsky coef ficients;    continued fractions;    Carath´eodory functions;    hypergeometric functions;   

DOI  :  10.3842/SIGMA.2016.075

来源: National Academy of Science of Ukraine

【 摘 要 】

Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogonal polynomials and the associated Szegő polynomials are analyzed. Two illustrations, one involving Gaussian hypergeometric functions and the other involving Carathéodory functions are also provided. A connection between these two illustrations by means of complementary chain sequences is also observed.

【 授权许可】

Unknown