The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. Modified generating functions of orthogonal polynomials are shown to generate polynomials satisfying recurrences of known degree greater than three. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.
Bibliographical noteFunding Information:
The first author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2013R1A1A2061006 ). The second author was supported by National Science Foundation grant DMS-1148634 .
© 2014 Elsevier Inc.
- Askey-Wilson polynomials
- Hermite polynomials
- Orthogonal polynomials