For corresponding formulas for Chebyshev, Legendre, and the Hermite
polynomials apply (18.7.3)–(18.7.6),
(18.7.9), and
(18.7.11).
Note. The first of each of equations (18.5.7) and
(18.5.8) can be regarded as definitions of
when the conditions and
are not satisfied. However, in these circumstances the
orthogonality property (18.2.1) disappears. For this reason, and
also in the interest of simplicity, in the case of the Jacobi polynomials
we assume throughout this chapter that
and , unless stated otherwise. Similarly in
the cases of the ultraspherical polynomials
and the Laguerre polynomials we assume that
, and , unless
stated otherwise.