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You can use Series to specify the order of approximation. When an expression involving the output of Series, which is a SeriesData object, is evaluated, the calculus is done for you. sol = Solve[x^2 + (b + Epsilon)*x + c == 0, x] approx = sol /. Epsilon -> Series[Epsilon, {Epsilon, 0, 1}] // Normal Alternatively, you could apply Series to the ...


Well, the following meets your formal requirements evenFunction[f_][args__] := f[Abs /@ Unevaluated[args]] evenFunction[even][a, b, c] even[Abs[a], Abs[b], Abs[c]] But is it really better than evenFunction[f_][args__] := f @@ Abs[{args}] I, myself, would choose the 2nd version over the 1st. Update It is not necessary to set the attribute ...


You don't say explicitly how you want to handle terms of order zero. Assuming that these are also to be discarded expr = a x^3 + b x^2 + c x + d; minOrder = 2; coefList = CoefficientList[expr, x]; lenCoefList = Length[coefList]; Expand[(Expand[x*expr] /. ((x^n_ /; n > minOrder) -> $t^n) /. {x -> 0, $t -> x})/x] (* b x^2 + a x^3 *) ...


If you first SetOptions[Series, Analytic -> False] and then wrap f[x] in HoldForm, Series[HoldForm[f[x]]*Sin[x],{x,0,3}] then when you take this output and run it as an input, HoldForm[f[x]] is not expanded out.


You can executive the code in mma 10 or above version EntityClass["WolframLanguageSymbol", "Atomic"]//EntityList But is not all atomic function,as I know.


Normal@Series[your expression,{x,0,1}]


Defining a function like Clear[FactorByVariable] FactorByVariable[p_,c_]:=c Expand[p/c] will be one of the simpler options. The argument p is the polynomial you wish to factor from and c is the variable you wish to factor out. I think the reason you can't get your desired result with something like FactorTerms[a x + b x^2 + c x^3,{a,c,x}] is because ...


Convert both variables to the same, then evaluate as a series from infinity should work in most cases: A straightforward example for some function f = f(x,y): Series[f/.{x->q,y->q},{q,Infinity,2}] Of course this requires that both variables grow parametrically at the same rate. This also allows you to take different limits: x->1/q for example ...

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