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Date: 14-12-2021
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Jacobi-Gauss quadrature, also called Jacobi quadrature or Mehler quadrature, is a Gaussian quadrature over the interval with weighting function
(1) |
The abscissas for quadrature order are given by the roots of the Jacobi polynomials . The weights are
(2) |
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(3) |
where is the coefficient of in . For Jacobi polynomials,
(4) |
where is a gamma function. Additionally,
(5) |
so
(6) |
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(7) |
where
(8) |
The error term is
(9) |
(Hildebrand 1956).
REFERENCES:
Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 331-334, 1956.
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كيف تساهم الأطعمة فائقة المعالجة في تفاقم مرض يصيب الأمعاء؟
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