I'm trying to expand (q+1)/(q−3) at q=∞. This doesn't work:
sage: f=(q + 1)/(q - 3)
sage: f.series(q==infinity,3)
Order(-Infinity)This also doesn't:
sage: f.subs(q==1/q).series(q==0,3).subs(q==1/q)
-1/2/q - 1/2(the value is wrong, it should be 1 as q goes to infinity, not −1/2).
This works:
sage: f.subs(q==1/q).simplify_rational().series(q==0,3).subs(q==1/q)
4/q + 12/q^2 + 1But is not very friendly. Any ideas?
What about :
sage: var("q")
q
sage: f(q)=(q+1)/(q-3);f
q |--> (q + 1)/(q - 3)
sage: f.maxima_methods().powerseries(q,oo)
4*sum(3^(i1 - 1)/q^i1, i1, 0, +Infinity) - 1/3That's not what had in mind (an infinite sum), but using your approach this does work:
sage: f.maxima_methods().taylor(q,oo,2)
4/q + 12/q^2 + 1
After playing with it a bit more, I realized that sage has this too:
sage: f.taylor(q,oo,2)
4/q + 12/q^2 + 1So I consider the case closed (except for that fact that series should have done the same?)
Asked: 6 years ago
Seen: 364 times
Last updated: Jan 27 '19
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