Anzeige
Erschienen in:
2010 | OriginalPaper | Buchkapitel
Properties of Entire Functions
verfasst von : Joseph Bak, Donald J. Newman
Erschienen in: Complex Analysis
Verlag: Springer New York
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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
.