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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-3,
author = {Marek Bo\.zejko and Nizar Demni},
title = {Topics on Meixner families},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {61-74},
zbl = {1209.33019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-3}
}
Marek Bożejko; Nizar Demni. Topics on Meixner families. Banach Center Publications, Tome 89 (2010) pp. 61-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-3/