Christoffel-Darboux Formula
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
19-1-2019
1210
Christoffel-Darboux Formula
For three consecutive orders of an orthonormal polynomial, the following relationship holds for 
, 3, ...:
 |
(1)
|
where 
, 
, and 
are constants. Denoting the highest coefficient of 
by 
,
Then
 |
(5)
|
In the special case of 
, (5) gives
 |
(6)
|
REFERENCES:
Abramowitz, M. and Stegun, I. 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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