“Pollaczek Polynomial”的概念、定义、习题解题方法及翻译-数学辞典

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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