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I have the following functions:

f(XY)=g1(X)g2(Y)+g1(Y)g2(X)+h(XY)

h(X*Y)=h^2(X)*g1(Y)

where * in f is not necessery multiplication. How to find (symbolic)

f(X^7)?

I have the following functions:

   f(X*Y)=g1(X)g2(Y)+g1(Y)g2(X)+h(X*Y)

h(X*Y)=h^2(X)*g1(Y)

where * in f is not necessery multiplication. How to find (symbolic)

f(X^7)?

I have the following functions:

   f(X*Y)=g1(X)g2(Y)+g1(Y)g2(X)+h(X*Y)

h(X*Y)=h^2(X)*g1(Y)

where * in f is not necessery multiplication. How to find (symbolic)

f(X^7)?

I have the following functions:

   f(X*Y)=g1(X)g2(Y)+g1(Y)g2(X)+h(X*Y)
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)*g1(Y)

where * in f is not necessery multiplication. How to find (symbolic)

f(X^7)?

Suppose I have functions $f$, $g_1$, $g_2$, $h$ and an operation $*$, which is not necessarily multiplication, satisfying the following functions: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)*g1(Y)

where $$ h(X * in f is not necessery multiplication. Y) = h^2(X) * g1(Y) $$

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

f(X^7)?

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

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

$$ h(X * Y) = h^2(X) * g1(Y) g_1(Y) $$

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