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A note on simultaneous polynomial approximation of exponential functions
Published online by Cambridge University Press: 17 April 2009
Abstract
Let α1, …, αm be distinct complex numbers and τ(1), …, τ(m) be non-negative integers. We obtain conditions under which the functions
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
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).
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 333 - 338
- Copyright
- Copyright © Australian Mathematical Society 1974
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