For the definitions of , , and see §16.2.
and two similar formulas by symmetry; compare the second row in Table 18.6.1.
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.
For the corresponding polynomials of degrees 7 through 12 see Abramowitz and Stegun (1964, Tables 22.3, 22.5, 22.9, 22.10, 22.12).