1. The problem statement, all variables and given/known data Hi I have sometimes seen a function f being written as [tex] f \approx f_0 + \varepsilon f_1(x)+ \varepsilon^2 f_2(x) + \ldots [/tex] where [itex]f_0[/itex] is an equlibrium value and all higher-order terms are non-equilibrium values (not derivates!). The assumption has always been that [itex]\varepsilon \ll 1[/itex]. My question is: Mathematically, I guess we are expanding the function f around its equlibrium value. But when I look at the expression for a Taylor expansion, I can't make this fit with anything. Are we non-mathematicians even allowed to write the function like this?