The numerical solution of an infinite set of linear simultaneous equations
valid for e > 0, and, actually, for Re(t) > —k. 3. The expansion for the associated characteristic function. Consider the solution of u" + A (e)[/(x) + eg(x)]u = 0, u(0) = 0, u'( 0) = 1. The classical iteration procedure for obtaining u shows that u is an analytic function of A(e) and e for 0 < x < 1, for all e and A(«). Consequently, u is an analytic function of a for Re(t) > b, uniformly in 0 < x < 1, and thus possesses an expansion