On a family of hypergeometric Sobolev orthogonal polynomials on the unit circle

2020/02/15 by Zagorodnyuk, Sergey M.
#33C45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.06428

Abstract

In this paper we study the following family of hypergeometric polynomials: y_n(x) = ( (-1)^ρ)/( n! ) xⁿ ₂ F₀(-n,ρ;-;-(1)/(x)), depending on a parameter ρ∈ℕ. Differential equations of orders ρ+1 and 2 for these polynomials are given. A recurrence relation for y_n is derived as well. Polynomials y_n are Sobolev orthogonal polynomials on the unit circle with an explicit matrix measure.

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