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单词 Pollaczek Polynomial
释义

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.


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