A moment problem and a family of integral evaluations
Abbreviated Journal Title
Trans. Am. Math. Soc.
indeterminate moment problems; q(-1)-hermite polynomials; Al-Salam-Chihara polynomials; biorthogonal rational functions; divided; difference operators; raising and lowering operators; Bethe Ansatz; equations; integral operators; CLASSICAL ORTHOGONAL POLYNOMIALS; ASKEY-WILSON OPERATOR; Q-HERMITE; POLYNOMIALS; Q-BETA-INTEGRALS; INVERSE; Mathematics
We study the Al-Salam-Chihara polynomials when q > 1. Several solutions of the associated moment problem are found, and the orthogonality relations lead to explicit evaluations of several integrals. The polynomials are shown to have raising and lowering operators and a second order operator equation of Sturm-Liouville type whose eigenvalues are found explicitly. We also derive new measures with respect to which the Ismail-Masson system of rational functions is biorthogonal. An integral representation of the right inverse of a divided difference operator is also obtained.
Transactions of the American Mathematical Society
"A moment problem and a family of integral evaluations" (2006). Faculty Bibliography 2000s. 6030.