Abstract: The eigenvalue problem and expansion theorems associated with orr-Sommerfeld equation are fundamental for the investigation of the stability of laminar fluid motion and have been studied by many authors. Nevertheless, the results are still incomplete^[6]. In this paper, this problem is investigated again and some new results have been obtained, namely: (1) The expansion series converges uniformly and absolutely. (2) The co-officients of the expansion series satisfy an inequality of Paley-Wiener type, which is the natural extension of the well-known Bessel equality of a complete orthogonal set.

Key words: nonlinear, parameter iteration, approach solution