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I have some functional in Mathematica that depends on the functions (for example u1(x,y,t) u2(x,y,t) and others) and its derivatives.

I want to expand this functional in series of ε.

Its perturbation theory as you understand, and I should take into account that not only functions but also

derivatives (by themselfes) are also have scale, i.e (in my example) u1~u2~∂_{x}~∂_{y}~ε, ∂_{t}~ε^{2}and I want to get smth up to ε^{2}(like for example u1(x,y)+u2(x,y)+u1(x,y)*u2(x,y)+∂_{x}u1(x,y)+∂_{x}u2(x,y)+∂_{y}u1(x,y)+∂_{t}f(x,y))

How to do it?

Thank you very much!

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# Non trivial series in Matematica

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