I want to create Taylor series of a complex function that has complex conjugate in it. Obviously I cannot do a total derivative but derivations over real and imag parts exist.


Bonus question: Can I produce a Taylor series using only derivations over real part?



Taylor series of a complex function that is not holomorphic
Another option is $\sum c\_{mn}z^m \bar z^n$, which still keeps track of the complex structure. For instance, harmonic functions will have $c\_{mn}=0$ unless $mn=0$.


