Legendre-Gauss Quadrature

Also called ``the'' Gaussian Quadrature or Legendre Quadrature. A Gaussian Quadrature over theinterval with Weighting Function . The Abscissas for quadrature order aregiven by the roots of the Legendre Polynomials , which occur symmetrically about 0.The weights are

(1)

(2)

			(3)

(4)

(5)

(6)

(7)

(8)

2	± 0.57735	1.000000
3	0	0.888889
	± 0.774597	0.555556
4	± 0.339981	0.652145
	± 0.861136	0.347855
5	0	0.568889
	± 0.538469	0.478629
	± 0.90618	0.236927

The Abscissas and weights can be computed analytically for small .

2		1
3	0
4

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 462-463, 1987.

Chandrasekhar, S. Radiative Transfer. New York: Dover, pp. 56-62, 1960.

Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 323-325, 1956.

• Factorial Sum
• Factoring
• Factorion
• Factorization
• Factor Level
• Factor Ring
• Factor Space
• Fagnano's Point
• Fagnano's Problem
• Fagnano's Theorem
• Fair Game
• Fairy Chess
• Fallacy
• False
• False Position Method
• Faltung (Form)
• Faltung (Function)
• Fan
• Fano Plane
• Fano's Axiom
• Farey Sequence
• Farey Series
• Farkas's Lemma
• Faro Shuffle
• Far Out