### Abstract

Let α_{1}, …, α_{m} 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 a_{1} (z), …, a_{m} (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 a_{1} (z), …, a_{m} (z).

Original language | English |
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Pages (from-to) | 333-338 |

Number of pages | 6 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1974 |

Externally published | Yes |

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## Cite this

Loxton, J. H., & Van Der Poorten, A. J. (1974). A note on simultaneous polynomial approximation of exponential functions.

*Bulletin of the Australian Mathematical Society*,*11*(3), 333-338. https://doi.org/10.1017/S0004972700043963