PageHeader : Funkcialaj Ekvacioj, 4 (1962), 115?139 Title : Formal Solutions of a Linear Ordinary Title : Differential Equation of the nth Order Title : at a Turning Point AuthorInfo : By Yasutaka SIBUYA* AuthorInfo : (Ochanomizu University) section : I. Introduction subsection : 1 Main problem. Let an equation of the form subsection : 2 Orr-Sommerfeld equation. subsection : 3 Works of Wasow, Langer, Lin and Rabenstein. subsection : 4 Main theorem. subsection : 5 Remarks. section : II. Sketch of Proof subsection : 6 Recurrence formulas for $B_{k,h}$ . subsection : 9 Fundamental equations. subsection : . 10 Determinacy of the quantities $T_{k}$ and $Q_{v}$ . subsection : 11 Problem (P). subsection : 12 Remarks. section : III. Details of Proof subsection : 13 Equation (11. 10). subsection : 14 Determinacy of $H$ and $B$ . subsection : 15 Completion of proof. subsection : 16 Proof of lemmas. section : Bibliography