Orthogonal polynomials, Legendre
It is common to choose the normalization condition
\begin{equation*}
L_N(1)=1.
\end{equation*}
With these equations we can determine a Legendre polynomial of arbitrary order
with input polynomials of order
N-1 and
N-2 .
As an example, consider the determination of L_0 , L_1 and L_2 .
We have that
\begin{equation*}
L_0(x) = c,
\end{equation*}
with c a constant. Using the normalization equation L_0(1)=1
we get that
\begin{equation*}
L_0(x) = 1.
\end{equation*}