I spent half an hour to solve this problem with the aid of cauchy-rieman equations, but it did not work for me.
Can somebody help me to solve this problem descriptively ?
Thanks in advance
I'm not sure what you mean by , but if we write , then , and then , and since is analytic then
**
** , so
**
**
Now get, from symmetry, a similar expression for and adding both and after cancelling a lot of stuff (remember! by continuity of the 2nd partial derivative we have that and then same for the mixed der. of ) we get... , unless that "X" you wrote there has another meaning different from multiplication.
Tonio