An extension of the universal power series of Seleznev
Abstract
We show generic existence of power series a with complex coefficients an, such that the sequence of partial sums of a new power series where its coefficients bn are functions of a0, a1, ..., an approximate every polynomial uniformly on every compact set K not containing the origin and with connected complement. The functions bn are assumed to be continuous and such that for every complex numbers a0, a1, ... , an - 1, c there exists a complex number an such that bn(a0, a1,..., an-1, an) = c. This clearly covers the case of linear functions bn.
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