Re: [math-fun] Power series question
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 = 0.
Question: Does this function have a power series that converges in some neighborhood of x=0 ?
Does "power series" here mean Taylor expansion, or maybe Puiseux? The first looks pretty unlikely, given that |z| alone is not analytic! WFL On 8/25/18, Dan Asimov <dasimov@earthlink.net> wrote:
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 = 0.
Question: Does this function have a power series that converges in some neighborhood of x=0 ?
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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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Maybe. But sgn(x) x**2 On 26-Aug-18 07:40, James Propp wrote:
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 ?
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (4)
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Dan Asimov -
Fred Lunnon -
James Propp -
Mike Speciner