Complex Analysis: Theory and Applications · Problem 3.2.9

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · entire-functions

Problem

Show that the following functions are entire (see Definition 3.2). (a) f(z)=f(x+iy)=cosh⁡xsin⁡y−isinh⁡xcos⁡yf(z) = f(x+iy) = \cosh x \sin y - i\sinh x \cos y; (b) g(z)=g(x+iy)=cosh⁡xcos⁡y+isinh⁡xsin⁡yg(z) = g(x+iy) = \cosh x \cos y + i\sinh x \sin y.

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