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I'm looking for a function f(x,y) which has the following properties :

[tex]\frac{-\partial f}{\partial x}[/tex] tends to 0 when x or y tends to [tex]\pm \infty[/tex], odd in the x direction, and even in the y direction.

something that has a shape like [tex]exp(-(x^2 + y^2))*tanh(x)[/tex].

And [tex]\frac{\partial f}{\partial y}[/tex] has a shape that looks like [tex]exp(-(x^2+y^2))[/tex]

I'm looking for f, and not the derivative independantly because I want the divergence of the vector (df/dx, df/dy) to be 0.

can you help me ?

Thanks

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# Function to find

Can you offer guidance or do you also need help?

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