1.2 Racah

Definition.

 

where

and

Orthogonality.

 

where

and

Recurrence relation.

 

where

and

hence

and

Normalized recurrence relation.

 

where

Difference equation.

 

where

and

Forward shift operator.

 

or equivalently

 

Backward shift operator.

 

or equivalently

 

where

Rodrigues-type formula.

 

where

Generating functions. For we have

 

 

 

 

Remark. If we set , , , and in the definition (1.2.1) of the Racah polynomials we obtain the Wilson polynomials defined by (1.1.1) :

References. [43], [62], [64], [67], [69], [145], [274], [297], [301], [323], [331], [341], [343], [399].




Last modified on June 16, 1998