Topics on Meixner families
Volume 89 / 2010
Banach Center Publications 89 (2010), 61-74
MSC: 45L54, 37A50, 60G20, 33D45.
DOI: 10.4064/bc89-0-3
Abstract
We shed some light on the inter-connections between different characterizations leading to the classical Meixner family. This allows us to give free analogs of both Sheffer's and Al-Salam and Chihara's characterizations in the classical case by the use of the free derivative operator. The paper closes with a discussion of the $q$-deformed case, $|q| < 1$.
