MAXIMUM MODULUS, MAXIMUM TERM AND INTERPOLATION ERROR OF AN ENTIRE FUNCTION

Abstract

Let f be analytic on the compact set E Ì C , of positive transfinite diameter and let Cr
denote the largest equipotential curve of E such that f is analytic within Cr. Generally, the growth of an
entire function is measured in terms of its order and type. Here we have established the relations
between maximum modulus, maximum term and interpolation error of best uniform approximation to
a function f ÎC(E) = { f holomorphic on int (E) and continuous on E } by algebraic polynomials
and Lagrange polynomials, in the form of direct estimates