Category:Examples of Orthogonal Polynomials

This category contains examples of Orthogonal Polynomials.

Let $S$ be a set of polynomials over the real numbers $\R$:

$S = \set {\map {p_0} x, \map {p_1} x, \map {p_2} x, \ldots}$

such that $p_n$ is of degree $n$.

The elements of $S$ are orthogonal with respect to a closed real interval $\closedint a b$ and a continuous non-negative weight function $\map w x$ on $\closedint a b$ if and only if:

$\ds \int_a^b \map w x \map {p_i} x \map {p_j} x \rd x = 0$

for all $i \ne j$.