Also called Hermite Quadrature. A Gaussian Quadrature over the interval
with
Weighting Function . The Abscissas for quadrature order are given by the
roots of the Hermite Polynomials , which occur symmetrically about 0. The
Weights are
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
(9) |
2 | ± 0.707107 | 0.886227 |
3 | 0 | 1.18164 |
± 1.22474 | 0.295409 | |
4 | ± 0.524648 | 0.804914 |
± 1.65068 | 0.0813128 | |
5 | 0 | 0.945309 |
± 0.958572 | 0.393619 | |
± 2.02018 | 0.0199532 |
The Abscissas and weights can be computed analytically for small .
2 | ||
3 | 0 | |
4 | ||
References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 464, 1987.
Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 327-330, 1956.
© 1996-9 Eric W. Weisstein