An extension of the universal power series of Seleznev

Konstantinos Maronikolakis; Vassili Nestoridis

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arXiv · 1905.10556

An extension of the universal power series of Seleznev

Konstantinos Maronikolakis·Vassili Nestoridis

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Abstract

We show generic existence of power series a with complex coefficients a_n, such that the sequence of partial sums of a new power series where its coefficients b_n are functions of a_0, a_1, ..., a_n approximate every polynomial uniformly on every compact set K not containing the origin and with connected complement. The functions b_n are assumed to be continuous and such that for every complex numbers a_0, a_1, ... , a_{n - 1}, c there exists a complex number a_n such that b_n(a_0, a_1,..., a_{n-1}, a_n) = c. This clearly covers the case of linear functions b_n.

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Konstantinos Maronikolakis, Vassili Nestoridis. 2019-05-25. An extension of the universal power series of Seleznev. https://arxiv.org/abs/1905.10556

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