Complex conjugate of a derivative wrt z

[stallm]

First post!

Is it true that for a complex function f({z},\overline{z})

\overline{\frac{∂f}{∂z}} =\frac{∂\overline{f}}{∂\overline{z}}

I think I proved this while trying to solve a problem. If it turns out it's not true and I've made a mistake, I'll upload my 'proof' and have the mistakes pointed out :)

Thanks

 

[tiny-tim]

welcome to pf!

hi stallm!welcome to pf!

but if f(z,z*) = z* then ∂f/∂z = 0

 

[stallm]

hi stallm!welcome to pf!

but if f(z,z*) = z* then ∂f/∂z = 0

That would be alright, because f*=z, so ∂(f*)/∂(z*) =0, so the formula works for this function

 

[tiny-tim]

ah, i misread it

in that case, yes …

it's f(x,y), you're swapping x and y, differentiating wrt x instead of y, and swapping back again (for ∂f/∂z = (∂f*/∂z*)*) ​

 

[stallm]

Thank you!

 

[jackmell]

First post!

Is it true that for a complex function f({z},\overline{z})

\overline{\frac{∂f}{∂z}} =\frac{∂\overline{f}}{∂\overline{z}}

I think I proved this while trying to solve a problem. If it turns out it's not true and I've made a mistake, I'll upload my 'proof' and have the mistakes pointed out :)

Thanks

I do not think this is correct.