3.11 Big q-Laguerre

Definition.

 

Orthogonality. For and b < 0 we have

 

Recurrence relation.

 

where

Normalized recurrence relation.

 

where

q-Difference equation.

 

where

and

Forward shift operator.

 

or equivalently

 

Backward shift operator.

 

or equivalently

 

where

Rodrigues-type formula.

 

Generating functions.

 

 

 

Remark. The big q-Laguerre polynomials defined by (3.11.1) and the affine q-Krawtchouk polynomials given by (3.16.1) are related in the following way :

References. [13], [27], [228].




Last modified on July 6, 1998