3.23 q-Charlier

Definition.

 

Orthogonality.

 

Recurrence relation.

 

where

Normalized recurrence relation.

 

where

q-Difference equation.

 

Forward shift operator.

 

or equivalently

 

Backward shift operator.

 

or equivalently

 

where

Rodrigues-type formula.

 

where

Generating functions.

 

 

Remark. The q-Charlier polynomials defined by (3.23.1) and the q-Laguerre polynomials given by (3.21.1) are related in the following way :

References. [28], [67], [193], [208], [261], [323], [410].




Last modified on July 6, 1998