Hello all,
I'm trying to check a property of so-called 'Koornwinder-Dubiner'
polynomials. According to
http://www.springerlink.com/content/1l4h576r307l62n6/
they are defined over the reference triangle {r,s>=-1 and r+s <= 0} as
a:2*(1+r)/(1-s)-1;
b:s;
psi(r,s):=sqrt((2*i+1)*(i+j+1)/2)*jacobi_p(i,0,0,a)*((1-s)/2)^i*jacobi_p(j,2*i+1,0,b);
for certain i and j. According to the literature, these
polynomials are orthonormal with respect to the L2-norm over
the reference triangle, so I compute (i choose i=j=1):
i:1;
j:1;
integrate(integrate((psi(r,s))^2, r, -1, -s), s, -1, -1);
and maxima returns 0 for the result of this integral, which is
not what I expect for a polynomial that is orthonormal. I would
expect 1 there.
Is maxima giving me a wrong answer here, or am I misunderstanding
something?
Regards,
Bart
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