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On the Polynomials Orthogonal on Regular Polygons

✍ Scribed by Alexei Zhedanov

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
117 KB
Volume
97
Category
Article
ISSN
0021-9045

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✦ Synopsis

The two-parameter Pastro Al-Salam Ismail (PASI) polynomials are known to be bi-orthogonal on the unit circle with continuous weight function when 0<q<1. We study the case of q a root of unity. It is shown that corresponding PASI polynomials are orthogonal on the unit circle with discrete measure located on the vertices of the regular N-gon. Cases leading to a positive weight function are analyzed. In particular, we obtain trigonometric analogs of the Askey Szego polynomials which are orthogonal on regular N-gons with positive weight function.

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