Series of Polynomials

Abstract

IN many problems of pure and applied mathematics it is required to express a given function in terms of certain polynomials, such as those associated with the names of Legendre and Hermite. The general theory of all polynomials that can be used in this way engaged the attention of several mathematicians, including Prof. J. M. Whittaker of Liverpool. In the dark days of 1942-43 Major Whittaker, as he was then, found himself stationed in the vicinity of the University of Cairo. Stimulated by contact with the active mathematicians of that University, he started to deliver a course of lectures on the subject of his peace-time research. The course was cut short when he was transferred to another theatre of war. The lectures delivered were edited by Prof. Mursi, of the Fouad I University, Cairo, and published in pamphlet form by the Faculty of Science of that University. They deal with simple and other basic series, Cannon series, series effective on a circle, representation near a point, algebraic theory (using matrices), uniqueness, convergence, integral functions, and successive derivatives.