A very unexpected result for a Taylor Series
- To: mathgroup at smc.vnet.net
- Subject: [mg9768] A very unexpected result for a Taylor Series
- From: Wretch <arc at astro.columbia.edu>
- Date: Tue, 25 Nov 1997 00:07:17 -0500
- Organization: Vacuum
- Sender: owner-wri-mathgroup at wolfram.com
Hello all--last night I asked Mathematica3.0 to perform a Taylor series
expansion in the usual manner. The function being tailored was a
slightly complicated heap of fractional powers involving the variable
being expanded, as the function arose as a root of a cubic polynomial.
I expected there could be trouble due to the fractional powers, but I
figured Mathematica could handle any limits involved (L'Hopital's rule,
etc.).
Now, suppose we call the expanded function F[q]. I typed in
blah = Series[F[q],{q,0,3}] ,
and it returned fractional powers of q in the alleged Taylor series. The
output was
a q^{1/3} + b q + c q^{5/3} + d q^{7/3} + O(q^{10/3}) ,
where a,b,c,d are ugly looking constants.
So, it truncated before it got past powers higher than 3, but what's
with the appearance of these fractional powers? Any advice?
Thanks in advance.
AC