数值积分Legendre多项式MATLAB [英] Numerical integration Legendre Polynomials MATLAB

问题描述

Legendre多项式在MATLAB中作为矢量实现，您还可以在所有特定点x上获得所有关联的Legendre多项式.因此，我不知道如何在积分中使用这些功能.我的问题是:

The Legendre polynomials are implemented in MATLAB as vectors, where you also get all the associated Legendre polynomials evaluated at a particular point x. Thus, I don't know how I can use these functions inside an integral. My question is:

我该如何在Matlab的第n个Legendre多项式中计算从-1到1的(NUMALICALCALCUALTED(！))积分?

How can I evaluate the (NUMERICALLY CALCUALTED(!)) integral from -1 to 1 over the n-th Legendre polynomial in Matlab?

当我收到的答案实际上不是我想要的答案:我想在MATLAB中使用Legendre多项式的实现，因为其他建议可能会非常不稳定.

As I received an answer that is really not what I want: I want to use the implementation of the Legendre polynomials in MATLAB cause other suggestions may be highly unstable.

推荐答案

n=3 % degree of Legendre polynomial
step=0.1 % integration step
trapz(legendre(n,-1:step:1)')*step

这应该做你想要的

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