Help me please to prove this one:

Let us $\displaystyle f(z)\; and \; z^{5}\ \overline{f}(z)$ both are entire functions.

Prove that$\displaystyle f(z)$ is constant function necessarily.

Thanks

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- Aug 30th 2010, 01:14 PMsinichkocomplex analysis
Help me please to prove this one:

Let us $\displaystyle f(z)\; and \; z^{5}\ \overline{f}(z)$ both are entire functions.

Prove that$\displaystyle f(z)$ is constant function necessarily.

Thanks - Aug 31st 2010, 10:06 AMMauritzvdworm
The only way I can see this happening is to show that f is bounded, the result then follows from Liouville's theorem