I hava a orthogonal basis {1, t, , }
and this normalized is
{1,t, , }
I dont understand how they have done this. Any help would be much appreciated. Thanks.
You should tell us what interval these are supposed to be orthonormal over.
The usual norm for real functions over such an interval is:
If you have not made any typos I could work out what interval is implied by the given normalisations, but then you could just tell us.
CB
In the case of these Legendre polynomials, the purpose of that "normalisation" is not to make them orthonormal, but to ensure that they have the value 1 when t = 1. See that Wikipedia link for further information.