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单词 Jacobi-Gauss Quadrature
释义

Jacobi-Gauss Quadrature

Also called Jacobi Quadrature or Mehler Quadrature. A Gaussian Quadrature over the interval with Weighting Function . The Abscissas for quadrature order are given by the roots of the Jacobi Polynomials . The weights are

 
 (1)

where is the Coefficient of in . For Jacobi Polynomials,
(2)

where is a Gamma Function. Additionally,


(3)

so


(4)
 (5)

where
(6)

The error term is


(7)

(Hildebrand 1959).


References

Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 331-334, 1956.


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