Orthogonal polynomials and the moment problem - Steere, Henry Roland (My University, 2012)
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.
Keywords: Orthogonal polynomials.; Moment problems (Mathematics)