Laguerre-Gauss Quadrature

Also called Gauss-Laguerre Quadrature or Laguerre Quadrature. A Gaussian Quadrature overthe interval with Weighting Function . The Abscissas for quadrature order aregiven by the Roots of the Laguerre Polynomials . The weights are

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Beyer (1987) gives a table of Abscissas and weights up to .

2	0.585786	0.853553
	3.41421	0.146447
3	0.415775	0.711093
	2.29428	0.278518
	6.28995	0.0103893
4	0.322548	0.603154
	1.74576	0.357419
	4.53662	0.0388879
	9.39507	0.000539295
5	0.26356	0.521756
	1.4134	0.398667
	3.59643	0.0759424
	7.08581	0.00361176
	12.6408	0.00002337

The Abscissas and weights can be computed analytically for small .

2

For the associated Laguerre polynomial with Weighting Function ,

(10)

(11)

(12)

(13)

References

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

Chandrasekhar, S. Radiative Transfer. New York: Dover, pp. 64-65, 1960.

Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 325-327, 1956.

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