Consider the infinite series of polynomials $e_0(x), e_1(x), e_2(x), \ldots $ where $e_n(x)=x^n-1.$ I want to orthogonalise them, so I am looking for the range $[a,b]$ and for a weight function $w(x)$ such that $$ \int_a^b e_n(x) e_m(x) w(x)=\delta_{n,m} $$ I have tried to search for $w(x)$ as a polynomial and as series but not with any success. Any ideas?
2026-03-28 02:42:02.1774665722
How to orthogonalize polynomials?
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