Gauss-Legendre Quadrature

Number of
Sampling Points		iξiwi
110.000000000000000000002.00000000000000000000
21-0.577350269189625764511.00000000000000000000
20.577350269189625764511.00000000000000000000
31-0.774596669241483377040.55555555555555555555
20.000000000000000000000.88888888888888888888
30.774596669241483377040.55555555555555555555
41-0.861136311594052575220.34785484513745385737
2-0.339981043584856264800.65214515486254614262
30.339981043584856264800.65214515486254614262
40.861136311594052575220.347854845137453857371
51-0.906179845938663992800.23692688505618908751
2-0.538469310105683091030.47862867049936646804
30.000000000000000000000.56888888888888888888
40.538469310105683091030.47862867049936646804
50.906179845938663992800.23692688505618908751
61-0.932469514203152027810.17132449237917034504
2-0.661209386466264513660.36076157304813860757
3-0.238619186083196908630.46791393457269104739
40.238619186083196908630.46791393457269104739
50.661209386466264513660.36076157304813860757
60.0.932469514203152027810.17132449237917034504

Q&A
References
  1. Hammer, P. C., Marlowe, O. P., and Stroud, A. H. (1956). "Numerical integration over simplexes and cones", Math. Tables Aids Comp., 10, 130-137.
  2. Zienkiewicz, O. C. (1971) The Finite Element Method in Engineering Science, 2nd ed., McGraw-Hill, London.