Abstract
Let the rational function f(z) be represented as the ratio of two relatively prime polynomials: f(z)=p(z)/q(z) where d’ is the degree of p(z) and d“ the degree of q(z). We define the degree of the rational f (z) as d = max(d’,d”). It can be shown that this degree is the same as the Brouwer degree obtained when f (z) is regarded as a continuous mapping of the Riemann sphere into itself.
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© 1974 Springer-Verlag Berlin Heidelberg
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Donoghue, W.F. (1974). Preliminaries. In: Monotone Matrix Functions and Analytic Continuation. Die Grundlehren der mathematischen Wissenschaften, vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65755-9_1
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DOI: https://doi.org/10.1007/978-3-642-65755-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65757-3
Online ISBN: 978-3-642-65755-9
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