For (18.6.1) see Szegő (1975, (5.1.7)).
For Table 18.6.1, Rows 2, 4, 10, see Szegő (1975, (4.1.3),
(4.1.1), (4.7.4), (2.3.3), (4.7.3), (5.5.5));
the entries in the fourth and fifth columns of Rows 3 and 4 of Table
18.6.1 follow from (18.5.9) combined (for
Row 3) with (18.7.2);
the other entries of Row 3 of Table 18.6.1 are the case
of Row 2;
Rows 5–8 follow from (18.5.1)–(18.5.4);
Row 9 is the case of Row 3.
The DLMF now adopts the definitions for the Chebyshev polynomials
of the third and fourth kinds ,
used in Mason and Handscomb (2003). Therefore , ,
having been interchanged, Rows 6 and 7 have been modified accordingly.
For further details see Errata.