Expand all
Collapse all
|
Results 1 - 1 of 1 |
1. CJM 2002 (vol 54 pp. 709)
|
$q$-Integral and Moment Representations for $q$-Orthogonal Polynomials We develop a method for deriving integral representations of certain
orthogonal polynomials as moments. These moment representations are
applied to find linear and multilinear generating functions for
$q$-orthogonal polynomials. As a byproduct we establish new
transformation formulas for combinations of basic hypergeometric
functions, including a new representation of the $q$-exponential
function $\mathcal{E}_q$.
Keywords:$q$-integral, $q$-orthogonal polynomials, associated polynomials, $q$-difference equations, generating functions, Al-Salam-Chihara polynomials, continuous $q$-ultraspherical polynomials Categories:33D45, 33D20, 33C45, 30E05 |