NumericalDifferentialEquationAnalysis`
NumericalDifferentialEquationAnalysis`
GaussianQuadratureWeights
GaussianQuadratureWeights[n,a,b]
gives a list of the n pairs {xi,wi} of the elementary n-point Gaussian formula for quadrature on the interval a to b, where wi is the weight of the abscissa xi.
GaussianQuadratureWeights[n,a,b,prec]
attempts to give a result with prec digits of precision.
Details and Options
- To use GaussianQuadratureWeights, you first need to load the Numerical Differential Equation Analysis Package using Needs["NumericalDifferentialEquationAnalysis`"].
- Gaussian quadrature approximates the value of an integral as a linear combination of values of the integrand evaluated at optimal abscissas
: 
. - The abscissas are optimal in the sense that the quadrature formula is exact for all polynomials up to degree 2n-1.
Examples
Properties & Relations (1)Properties of the function, and connections to other functions
NIntegrate`GaussRuleData gives the same abscissas and weights as GaussianQuadratureWeights when the interval is from 0 to 1:
In[1]:=1
✖
https://wolfram.com/xid/0fggasdv7md9uqxvsgikf8m1njv8qd58efv979ztn-hm678y
Out[2]=2
If the interval range is different from 0 to 1, scaling the result of NIntegrate`GaussRuleData also gives the same result as GaussianQuadratureWeights:
In[3]:=3
✖
https://wolfram.com/xid/0fggasdv7md9uqxvsgikf8m1njv8qd58efv979ztn-bvx2i
Out[5]=5
