Let F(z) = i z. Then F is entire yet conj(F(z) = F(conj(z)) isn't an
identity.
In addition to entire, we need F to be real on the real axis in order that
conj(F(z) = F(conj(z)) is an identity.
Stavros wrote:
>> that conj(F(x))=F(conj(x)) -- which is true of analytic functions, but
>> not of all non-analytic functions. It also implicitly assumes that all
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