We describe various aspects of the Al-Salam-Chihara q-Laguerre polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial interpretation of the linearization coefficients. It is remarkable that the corresponding moment sequence appears also in the recent work of Postnikov and Williams on enumeration of totally positive Grassmann cells.
Bibliographical noteFunding Information:
This work was partially supported by the French National Research Agency under the grant ANR-08-BLAN-0243-03.
- Al-Salam-Chihara polynomials
- Linearization coefficients
- q-Laguerre polynomials
- y-Version of q-Stirling numbers of the second kind