Compute Laguerre L2 norm
y=laguerre_norm(n)
a 1-by-1 matrix of doubles, integer value, n>=0.
a matrix of doubles, the norm
Returns the integral:
where Ln is Laguerre polynomial and w is the Laguerre weight.
I=laguerre_norm(0) // Norm of L0 I=laguerre_norm(1) // Norm of L1 I=laguerre_norm(2) // Norm of L2 // Check that int Ln(x)^2 w(x) dx=1 // for w(x)=exp(-x) function y=sqLw(x, n) w=laguerre_weight(x) Px=laguerre_eval(x,n) y=Px^2*w endfunction for n = 1:5 [v,err]=intg(0,100,list(sqLw,n)); I=laguerre_norm(n); mprintf("n=%d, I=%f, v=%f\n",n,I,v) end | ![]() | ![]() |