Abstract
Because
and |g(z)| is bounded, Liouville’s theorem implies g is a constant. Since lim |z|→∞g(z)≡f(0).
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© 1992 Springer Science+Business Media New York
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Gelbaum, B.R. (1992). Entire Functions. In: Problems in Real and Complex Analysis. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0925-6_25
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DOI: https://doi.org/10.1007/978-1-4612-0925-6_25
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6949-6
Online ISBN: 978-1-4612-0925-6
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