Abstract
We now show that if f is entire and if\( g(z) = \left\{ {\begin{array}{*{20}{c}} {f(z) - f(a)} & {z \ne a} \\{f'(a)} & {z = a} \\ \end{array} } \right. \)then the Integral Theorem (4.15) and Closed Curve Theorem (4.16) apply to g as well as to f. (Note that since f is entire, g is continuous; however, it is not obvious that g is entire.)We begin by showing that the Rectangle Theorem applies to g.
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Bak, J., Newman, D.J. (2010). Properties of Entire Functions. In: Complex Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7288-0_5
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DOI: https://doi.org/10.1007/978-1-4419-7288-0_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7287-3
Online ISBN: 978-1-4419-7288-0
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