Given a function f[x]
, I would like to have a function leadingSeries
that returns just the leading term in the series around x=0
. For example:
leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)]
x
and
leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)]
-(1/(16 x^3))
Is there such a function in Mathematica? Or maybe one can implement it efficiently?
EDIT
I finally went with the following implementation, based on Carl Woll's answer:
lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal)
The advantage is, that this one also properly works with functions whose leading term is a constant:
lds[Exp[x],x]
1