I am pretty sure you can derive Taylor expansions for x>0 and for x<0. Proving that they coincide may take some work, or it may follow from some clever change of variables. Jim On Saturday, August 25, 2018, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Does "power series" here mean Taylor expansion, or maybe Puiseux? The first looks pretty unlikely, given that |z| alone is not analytic! WFL
A kind soul has pointed out my mismatched parentheses. Aaargh.
It should read as follows:
----- Graphing the function
f(x) = sgn(x) * |x|^(-1/(x-1))
over the domain (-1, 1) - {0} makes it appear quite smooth around x = 0.
Question: Does this function have a power series that converges in some neighborhood of x=0 ? -----
As always: Sorry about that.
—Dan
-----
On 25-Aug-18 17:41, Dan Asimov wrote:
Graphing the function
f(x) = sgn(x) * |x|^(-1/x-1))
over the domain (-1, 1) - {0} makes it appear quite smooth around x =
On 8/25/18, Dan Asimov <dasimov@earthlink.net> wrote: 0.
Question: Does this function have a power series that converges in some neighborhood of x=0 ?
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