On the Asymptotic Forms of the Solutions of Ordinary Linear Differential Equations of the Third Order in a Region Containing a Turning Point

The parameter X (complex) is large in absolute value.Thus |X| >iV, with some large constant N. LetThe function <p(z) is of the form zU2<px(z) with <fo(z) analytic and bounded from zero.Therefore <£(z) is of the form z3/2#i(z), with $i(z) analytic and bounded from zero in some neighborhood of z = 0. We shall reduce the given z-region, if necessary, so that 4>i(z) is bounded from zero within it.The function ^(z)