Hi,
I want to apply a complex differential operator to an expression "polynomial in the imaginary part * differential operator".
I have been unable to figure out how to do that using a formal operator and a concrete one that takes care of differentiating the polynomial.
In more detail:
Let $d$ be (my complex number is $x+iy$)
$d:=\frac{\partial}\partial x}- i\frac{\partial}{\partial y}$
which I want to apply to
$p(y) d$
where $p(y)$ is (an explicitly given) polynomial in y.
I would be happy about any suggestions! Thanks a lot!