The Behavior of a Complex Function at Infinity

Karl Menger
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Karl Menger: Illinois Institute of Technology

A chapter in Selecta Mathematica, 2003, pp 47-48 from Springer

Abstract: Abstract Traditionally, the behavior at ∞ of a complex function f is defined as the behavior at 0 of the function obtained by substituting the —1st power into f. This definition adequately describes the class of values f(z) for large z. For instance, the range near ∞of the identity function j (whose value for any z is j(z)=z) coincides with the range near 0 of the function j -1. But that definition does not in any way describe the structural behavior of f near ∞, reflected in properties of the class of pairs (z, f (z)) for large z. In fact, the association of the value f(z) with z may, by the substitution of j -1, completely change its character. For instance, the derivative of j near ∞ is the constant function 1, whereas that j -1 of near 0 goes even faster to ∞ than does j -1

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7091-6045-9_6

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DOI: 10.1007/978-3-7091-6045-9_6

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