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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"}]

enter image description here

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  • $\begingroup$ The Asymptotic is being done with the wrong variable. Use s rather than x $\endgroup$
    – Bob Hanlon
    Mar 3 at 2:00
  • $\begingroup$ 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 $\endgroup$
    – Yaroslav Bulatov
    Mar 3 at 2:06
  • $\begingroup$ Use Series[expr, {s, 0, 1}] // Normal to get -((9 s)/10) + Log[10] $\endgroup$
    – Bob Hanlon
    Mar 3 at 2:23

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