On the Krall-type Askey-Wilson Polynomials
R. Alvarez-Nodarse, R. Sevinik-Adiguzel
TL;DR
This paper introduces a new family of Krall-type Askey-Wilson polynomials obtained by adding mass points to the weight function, and explores their properties including recurrence relations and hypergeometric representations.
Contribution
It presents the first construction and analysis of Krall-type Askey-Wilson polynomials with added mass points at ±1, expanding the family of orthogonal polynomials.
Findings
Derived the three-term recurrence relation for the new polynomials
Expressed the polynomials as basic hypergeometric series
Analyzed properties of the Krall-type Askey-Wilson polynomials
Abstract
In this paper the general Krall-type Askey-Wilson polynomials are introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points . Several properties of such new family are considered, in particular the three-term recurrence relation and the representation as basic hypergeometric series.
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