The Local Growth of Power Series: A Survey of the Wiman-Valiron Method

Source abstract

Suppose that 1.1 is a transcendental integral function. In this article we develop the theory initiated by Wiman [22, 23] and deepened by other writers including Valiron [18, 19, 20], Saxer [15], Clunie [4, 5] and Kövari [10, 11], which describes the local behaviour of f ( z ), near a point where | f ( z ) | is large, in terms of the power seriesf of f ( z ).