Orthogonal Polynomials Associated with Complementary Chain Sequences

Kiran Kumar Behera ; A. Sri Ranga ; A. Swaminathan

Symmetry, integrability and geometry: methods and applications, Tome 12 (2016)

Résumé

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.

Détail

Keywords: chain sequences; orthogonal polynomials; recurrence relation; Verblunsky coefficients; continued fractions; Carathéodory functions; hypergeometric functions.

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