TY - JOUR
T1 - A note on simultaneous polynomial approximation of exponential functions
AU - Loxton, J. H.
AU - Van Der Poorten, A. J.
PY - 1974
Y1 - 1974
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84974023539&partnerID=8YFLogxK
U2 - 10.1017/S0004972700043963
DO - 10.1017/S0004972700043963
M3 - Article
AN - SCOPUS:84974023539
SN - 0004-9727
VL - 11
SP - 333
EP - 338
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 3
ER -