Normalization of JacobiP function

Dear;

I am new in MuPAD I would like to know if the matlab function JacobiP (which computes the Jacobi polynomial) is normalized to 1. To prove this I computed the following code:

syms x
a = 3.5;
b = 7.2;
P3 = jacobiP(3, a, b, x);
w = (1-x)^a*(1+x)^b;
int(P3*P3*w, x, -1, 1)

The answer is the symbolic expresion of the integral:

int((1 - x)^(7/2)*(x + 1)^(36/5)*(- (1284731*x^3)/16000 + (853923*x^2)/16000 + (44247*x)/16000 - 42439/16000)^2, x, -1, 1)

If the Jacobi polynomials are orthonormalized, the result should be 1 How can I evaluate this integral numerically? I tried (<http://es.mathworks.com/help/symbolic/mupad_ref/numeric-int.html>)

numeric::int(P3^2*w,x,-1,1)

or

numeric::int(P3^2*w,x,-1..1)

but Matlab return an error.

Many thanks in advance;

[Luis Isaac]

Thank you very much;

As can be seen the Matlab definition of JacoviP are not normalized.

So what is the normalization of the JacobiP, or how can I get orthonormalized Jacobi polynomilas whitout need to calculate the integral.

Thanks again;

[Torsten]

n=3;
a=3.5;
b=7.2;
normfactor=1/(2^(a+b+1)/(2*n+a+b+1)*gamma(n+a+1)*gamma(n+b+1)/(gamma(n+a+b+1)*gamma(n+1)));
fun=@(x) normfactor*jacobiP(n, a, b, x).^2.*(1-x).^a.*(1+x).^b;  
value=integral(fun,-1,1);

Best wishes

Torsten.

Answer 1

[Torsten]

a = 3.5;
b = 7.2;
fun=@(x) jacobiP(3, a, b, x).^2.*(1-x).^a.*(1+x).^b;
value=integral(fun,-1,1);

Best wishes

Torsten.