## Pollaczek Polynomial

Let , and write

 (1)

Then define by the Generating Function

 (2)

The Generating Function may also be written

 (3)

where is a Chebyshev Polynomial of the Second Kind. They satisfy the Recurrence Relation

 (4)

for , 3, ...with
 (5) (6)

In terms of the Hypergeometric Function ,
 (7)

They obey the orthogonality relation

 (8)

where is the Kronecker Delta, for , 1, ..., with the Weight Function
 (9)

References

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., pp. 393-400, 1975.