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