Orthogonal polynomials and the moment problem
Date
2012-10-01
Authors
Steere, Henry Roland
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Abstract
The classical moment problem concerns distribution functions on the real
line. The central feature is the connection between distribution functions
and the moment sequences which they generate via a Stieltjes integral. The
solution of the classical moment problem leads to the well known theorem
of Favard which connects orthogonal polynomial sequences with distribution
functions on the real line. Orthogonal polynomials in their turn arise
in the computation of measures via continued fractions and the Nevanlinna
parametrisation. In this dissertation classical orthogonal polynomials are investigated
rst and their connection with hypergeometric series is exhibited.
Results from the moment problem allow the study of a more general class
of orthogonal polynomials. q-Hypergeometric series are presented in analogy
with the ordinary hypergeometric series and some results on q-Laguerre
polynomials are given. Finally recent research will be discussed.