ABSTRACT
As in Chapter 6, zeros of f(z) are called turning points or transition points of the differential equation. We sometimes extend the name transition point to include singularities of]'(z) org(z). The forms of the approximate solutions of (I .O1) depend on the number and nature of the transition points. In the case in which I(u) or D(u) is free from transition points, which we shall refer to henceforth as Case I, we saw in Chapter 6 that the LG functions
f - 'I4(z) exp + u f ' I 2 (z) dz { S 1 furnish asymptotic solutions of (1.01) with uniform relative error O(u-') as (uI+ 03.
