3.20 Little q-Laguerre / Wall

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.

 

Generating function.

 

Remark. If we set and change q to we find the q-Laguerre polynomials defined by (3.21.1) in the following way :

References. [13], [25], [71], [121], [123], [124], [169], [193], [279], [280], [323], [392], [396].




Last modified on July 6, 1998