Abstract view
$q$Integral and Moment Representations for $q$Orthogonal Polynomials


Published:20020801
Printed: Aug 2002
Mourad E. H. Ismail
Dennis Stanton
Abstract
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, AlSalamChihara polynomials, continuous $q$ultraspherical polynomials
$q$integral, $q$orthogonal polynomials, associated polynomials, $q$difference equations, generating functions, AlSalamChihara polynomials, continuous $q$ultraspherical polynomials

MSC Classifications: 
33D45, 33D20, 33C45, 30E05 show english descriptions
Basic orthogonal polynomials and functions (AskeyWilson polynomials, etc.) unknown classification 33D20 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions] Moment problems, interpolation problems
33D45  Basic orthogonal polynomials and functions (AskeyWilson polynomials, etc.) 33D20  unknown classification 33D20 33C45  Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions] 30E05  Moment problems, interpolation problems
