#8943: RuntimeError with series
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Reporter: casamayou | Owner: burcin
Type: enhancement | Status: new
Priority: trivial | Milestone: sage-4.4.2
Component: calculus | Keywords: series, taylor
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by casamayou:
Old description:
> The function *series* can not give the power series expansion of
> f(x)=(1+arctan(x))**(1/x) , while *taylor* succeeds. Note that the
> function f can be continuously extended at 0.
>
> {{{
> sage: taylor((1+arctan(x))**(1/x), x, 0, 3)
> 1/16*x^3*e + 1/8*x^2*e - 1/2*x*e + e
> sage: ((1+arctan(x))**(1/x)).series(x==0, 3)
> RuntimeError: power::eval(): division by zero
> }}}
New description:
The function *series* can not give the power series expansion of
f(x)=(1+arctan(x))**(1/x) , while *taylor* succeeds. Note that the
function f can be continuously extended at 0.
{{{
sage: taylor((1+arctan(x))**(1/x), x, 0, 3)
1/16*x^3*e + 1/8*x^2*e - 1/2*x*e + e
sage: ((1+arctan(x))**(1/x)).series(x==0, 3)
RuntimeError: power::eval(): division by zero
}}}
Subsidiary question: why the functions *taylor* and *series* perform
similar tasks, but differently?
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8943#comment:1>
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