Checking the Orthogonality of Legendre Functions through SCILAB

Legendre functions have an important property that is, they are orthogonal on the interval −1 ≤ x ≤ 1:


(where δmn denotes the Kronecker delta, equal to 1 if m = n and to 0 otherwise).

We can verify this result using Scilab.

To work with Legendre Polynomials we use the Scilab function legendre(n,m,x).

Which basically returns the value of the Associated Legendre Polynomial for a given value of m,n and x.
However, since I only wanted Legendre Polynomials so I’ll have to put m=0.

The following code returns the value of the integral, ∫Pm(x)*Pn(x)dx,

//Legendre Polynomials Orthogonality Verification
n=input("Enter n:");
m=input("Enter m:");
mprintf('∫P%i(x)*P%f(x)dx= %g\n',m,n,a);

Enter n:1
Enter m:1
∫P1(x)*P1.000000(x)dx= 0.666667

Enter n:5
Enter m:2
∫P2(x)*P5.000000(x)dx= 0

scilab code for legendre functions

PhD researcher at Friedrich-Schiller University Jena, Germany. I'm a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT and Machine Learning related apps and softwares from time to time. Can code in most of the popular languages. Like to share my knowledge in Physics and applications using this Blog and a YouTube channel.
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