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Date: 19-1-2019
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Date: 13-2-2019
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Date: 19-1-2019
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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 ,
(2) |
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(3) |
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(4) |
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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