“Christoffel-Darboux Formula”的概念、定义、习题解题方法及翻译-数学辞典

单词

Christoffel-Darboux Formula

释义

Christoffel-Darboux Formula

For three consecutive Orthogonal Polynomials

(1)

for

, 3, ..., where

, and

are constants. Denoting the highest Coefficient of

			(2)
			(3)

Then

(4)

In the special case of

, (4) gives

(5)

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 785, 1972.

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., pp. 42-44, 1975.

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