# Asymptotic returns expression unchanged instead of first-order approximation

I'm using Asymptotic to get first-order expansion of expr=Gamma[0, s/10] - Gamma[0, s], and it returns expr unchanged.

Any idea why?

expr = Gamma[0, s/10] - Gamma[0, s];
expr = Gamma[0, s/10] - Gamma[0, s];
asymptotic1 = Asymptotic[expr, {s, 0, 1}] (*returns Log[10] *)
asymptotic2 =
Asymptotic[
expr, {s, 0, 2}] (*returns -(9 s)/10+(99 s^2)/400+Log[10] *)
approx = -0.9 s + 2.3025;
Plot[{expr, approx}, {s, 0, 5}, PlotLegends -> {"original", approx},
AxesLabel -> {"s"}]


• The Asymptotic is being done with the wrong variable. Use s rather than x Mar 3 at 2:00
• Ooops fixed. So the curious thing is that Asymptotic[expr, {s, 0, 1}] gives 0th order approximation, while Asymptotic[expr, {s, 0, 2}] gives 2nd order, it doesn't give 1st order for some reason, but it seems it should exist Mar 3 at 2:06
• Use Series[expr, {s, 0, 1}] // Normal to get -((9 s)/10) + Log[10] Mar 3 at 2:23