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.

Pollaczek polynomials 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 weighting function