A note on simultaneous polynomial approximation of exponential functions

J. H. Loxton, A. J. Van Der Poorten

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Let α1, …, αm be distinct complex numbers and τ(1), …, τ(m) be non-negative integers. We obtain conditions under which the functions [formula omitted] form a perfect system, that is, for every set ρ(1), …, ρ(m) of non-negative integers, there are polynomials a1 (z), …, am (z) with respective degrees exactly ρ(1)−1, …, ρ(m)−1, such that the function [formula omitted] has a zero of order at least ρ(1) + … + ρ(m)−1 at the origin. Moreover, subject to the evaluation of certain determinants, we give explicit formulae for the approximating polynomials a1 (z), …, am (z).

Original languageEnglish
Pages (from-to)333-338
Number of pages6
JournalBulletin of the Australian Mathematical Society
Issue number3
Publication statusPublished - 1974
Externally publishedYes


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