Abstract
If f ∈ H(G), G a connected open set, it is a consequence of the power series expansion for holomorphic functions that if f(zn) = 0, zn → z0 ∈ G then f = 0 in G. It is also a consequence that if f(n)(z0) = 0 for n = 0,1,2,…, then f = 0 in G. We adopt conventions about “sets with multiplicity” that allow us to treat both cases as one.
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© 1984 Springer-Verlag New York Inc.
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Luecking, D.H., Rubel, L.A. (1984). Runge’s Theorem. In: Complex Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8295-9_10
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DOI: https://doi.org/10.1007/978-1-4613-8295-9_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90993-6
Online ISBN: 978-1-4613-8295-9
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