Is there a standard term for functions $f\colon \mathbb{C} \to \mathbb{C}$ with the property that $f(\overline{z}) = \overline{f(z)}$ for all $z$? Examples include analytic/meromorphic functions with only real coefficients in their Taylor/Laurent series, and intuitively, any function whose definition doesn't explicitly break the symmetry between $i$ and $-i$.

Related: Complex Conjugate of Complex function, Name for operators that commute with conjugation?, Schwarz reflection principle.

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    $\begingroup$ They are called real ( when there is no danger of confusion with real valued functions as this property means $f$ takes real values on the real numbers in its domain which could be a subset of the plane) or conjugate invariant $\endgroup$ – Conrad Aug 7 at 22:55
  • $\begingroup$ @Conrad Thanks! Do you know of a textbook or similar that uses those terms? $\endgroup$ – Elias Riedel Gårding Aug 8 at 14:11
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    $\begingroup$ those terms appear pretty much everywhere where complex analytic functions appear - the "real comes from polynomials as in that class, these are precisely polynomials with real coefficients $\endgroup$ – Conrad Aug 8 at 17:07

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