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

单词

Krawtchouk Polynomial

释义

Krawtchouk Polynomial

Let be a Step Function with the Jump

(1)

, 1, ...,

, where

, and

. Then

(2)

for

, 1, ...,

. It has Weight Function

(3)

where

is the Gamma Function, Recurrence Relation

(4)

and squared norm

(5)

It has the limit

(6)

where

is a Hermite Polynomial, and is related to the Hypergeometric Function by


	(7)

See also Orthogonal Polynomials

References

Nikiforov, A. F.; Uvarov, V. B.; and Suslov, S. S. Classical Orthogonal Polynomials of a Discrete Variable. New York: Springer-Verlag, 1992.

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., pp. 35-37, 1975.

Zelenkov, V. ``Krawtchouk Polynomial Home Page.'' http://www.isir.minsk.by/~zelenkov/physmath/kr_polyn/.

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