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arXiv · 1505.00742

Nevanlinna extremal measures for polynomials related to $q^{-1}$-Fibonacci polynomials

František Štampach
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Abstract

The aim of this paper is the study of $q^{-1}$-Fibonacci polynomials with $0<q<1$. First, the $q^{-1}$-Fibonacci polynomials are related to a $q$-exponential function which allows an asymptotic analysis to be worked out. Second, related basic orthogonal polynomials are investigated with the emphasis on their orthogonality properties. In particular, a compact formula for the reproducing kernel is obtained that allows to describe all the N-extremal measures of orthogonality in terms of basic hypergeometric functions and their zeros. Two special cases involving $q$-sine and $q$-cosine are discussed in more detail.

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BibTeXRIS

František Štampach. 2016-02-29. Nevanlinna extremal measures for polynomials related to $q^{-1}$-Fibonacci polynomials. https://doi.org/10.1016/j.aam.2016.02.005

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