Computational Methods and Function Theory 7 (2007), No. 2, 433--442
Copyright Heldermann Verlag 2007
James Langley
jkl@maths.nott.ac.uk , University of Nottingham, School of Mathematical Sciences, NG7 2RD, U.K.
A classical theorem of Pólya states that if $f$ is an entire function taking integer values at the non-negative integers and satisfying the growth condition f(z) = O(|z|M 2{|z|}) as z-> ∞, for some M > 0, then there exist polynomials P1, P2 with f(z) \equiv P1(z) 2z + P2(z). It is shown that the same result holds for functions analytic in a half-plane Re z ≥ A.
Keywords: Analytic functions, forward differences.
MSC 2000: 30D20,30D35.
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