Notes on the Extension of Aitken's Theorem (for Polynomial Interpolation) to the Everett Types.

Abstract

These notes are intended to be read in connexion with Dr A. C. Aitken's paper, Proc. Edinburgh Math. Soc. (2) 1 (1929), 199-203. It is proposed to show (by a simple line of direct algebraic demonstration which is also applicable to the original formula) that Aitken's Theorem can be extended to the Everett types, i.e. the types which include two sets of terms—one set involving u (0) and the resultant of generalised operations on u (0), and the other set involving u (1) and the resultant of similar operations on u (1).