I'd like to find the dominant terms of an expression given the conditions $x,y >> 1$:
$c_0 y+\frac{y^2 \left(4 c_0^2 y - 12 c_1 c_2^2+y^2\right)}{24 x^2 \left(\text{c1}^2+\text{c2}^2+y\right)}$
Is there an easy way to do this? I need the dominant terms for a given order O(x,y). It would be helpful to get the "small" contribution as a separate output. Thanks.
Series[(*expression here*), {x,Infinity,0},{y,Infinity,0}]
$\endgroup$x
vs.y
. $\endgroup$y=k*x
(or approximately equals) for some unspecified constantk!=0
then you can just replacey
withk*x
and take theSeries
. If they vary in an unspecified way e.g.y
could be on the order ofx^2
orx^(1/2)
orExp[x]
then your asymptotic behavior will behave quite differently in different regions of the parametrized space. $\endgroup$