Complex Analysis: Theory and Applications · Problem 7.2.8

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · taylor-series

Problem

Suppose that f(z)=∑n=0∞cnznf(z) = \displaystyle\sum_{n=0}^{\infty} c_n z^n is an entire function. ((a)) Find a series representation for f(zˉ)‾\overline{f(\bar{z})}, using powers of zz. ((b)) Show that f(zˉ)‾\overline{f(\bar{z})} is an entire function. ((c)) Does f(zˉ)‾=f(z)\overline{f(\bar{z})} = f(z)? Why or why not?

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