On Tuesday, May 24, 2016 at 9:03:51 AM UTC-7, saad khalid wrote: > > Hey everyone: > > So, I have the following function: > (2t^3+1)/((t^2+t+1)^2(t-1)^2) > > I want to take get the Laurent series expansion of it. It can be seen > through Wolfram Alpha here: > http://www.wolframalpha.com/input/?i=laurent+series+expansion+of+%282t > ^3%2B1%29%2F%28%28t^2%2Bt%2B1%29^2%28t-1%29^2%29 > > From my understanding, it's just the taylor series expansion at t = 1. I > try using the laurent_series function on sage as follows: > Your wolfram alpha output looks like an unreadable URL so I can't do anything with that, but it seems you want the laurent series expansion of this function at t=1. Since this function isn't regular at t=1, the function doesn't have a taylor expansion there, so the laurent series will not be equal to it (this function has only a finite order pole, so it has a laurent series expansion at t=1).
If you want to get the laurent series at t=1, you can introduce another variable, say w=t-1 (i.e., t=w+1) and expand in that: sage: R.<w>=LaurentSeriesRing(QQ) sage: t=w+1 sage: f = (2*t^3+1)/((t^2+t+1)^2*(t-1)^2) sage: f 1/3*w^-2 + 1/9 - 2/9*w + 2/9*w^2 - 4/27*w^3 + 5/81*w^4 - 7/243*w^6 + 8/243*w^7 - 2/81*w^8 + 10/729*w^9 - 11/2187*w^10 + 13/6561*w^12 - 14/6561*w^13 + 10/6561*w^14 - 16/19683*w^15 + 17/59049*w^16 + O(w^18) You cannot obtain the laurent series expansion of f at t=1 from only finitely many terms of the taylor expansion of f at t=0. There is not enough information. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
