# Functions with operation (multiplication) as argument

Suppose I have functions $f$, $g_1$, $g_2$, $h$ and an operation $*$, which is not necessarily multiplication, satisfying the following relations:

$$ f(X * Y) = g_1(X) g_2(Y) + g_1(Y) g_2(X) + f(X) * f(Y) + h(X * Y) $$

$$ h(X * Y) = h^2(X) * g_1(Y) $$

How to find a symbolic expression for $f(X^7)$?

I don't understand your question;

`f(X*Y) = ...`

does not seem to be valid Python syntax. Could you provide the full code of what you are trying to do?