For an infinite set of discrete values , , of the accessory parameter , the function is analytic at , and hence also throughout the disk . To emphasize this property this set of functions is denoted by
The eigenvalues satisfy the continued-fraction equation
in which are as in §31.3(i).
with , denotes a set of solutions of (31.2.1), each of which is analytic at and . The set depends on the choice of and .