3.9 q-Meixner-Pollaczek

Definition.

 

Orthogonality. For 0 < a < 1 we have

 

where

with

Recurrence relation.

 

Normalized recurrence relation.

 

where

q-Difference equation.

 

where

Forward shift operator.

 

or equivalently

 

Backward shift operator.

 

or equivalently

 

Rodrigues-type formula.

 

Generating functions.

 

 

References. [13], [20], [55], [64], [113], [217].




Last modified on July 6, 1998