= Solution
A sequence of real <orthogonal polynomials> consists of real polynomials $p_n$ with <degree of a polynomial> $n$ and
$$
\langle p_m,p_n\rangle=0\quad(m\ne n),\qquad \langle p_n,p_n\rangle>0.
$$
Orthogonality is relative to the specified <inner product>, rather than to the ordinary coefficients. A <monic polynomial> has leading coefficient one, so a <monic orthogonal polynomial> has the form $p_n(x)=x^n+\text{terms of lower degree}$. In particular, the monic degree-zero polynomial is $p_0=1$.
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