1.4 Continuous Hahn

Definition.

 

Orthogonality. If , and , then

 

Recurrence relation.

 

where

and

Normalized recurrence relation.

 

where

Difference equation.

 

where

and

Forward shift operator.

 

or equivalently

 

Backward shift operator.

 

or equivalently

 

where

Rodrigues-type formula.

 

Generating functions.

 

 

 

References. [41], [43], [67], [68], [76], [205], [260], [274], [299], [301], [303].




Last modified on June 16, 1998