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## Re: stable, numerical, maclaurin series of analytic functions

**From**: |
Przemek Klosowski |

**Subject**: |
Re: stable, numerical, maclaurin series of analytic functions |

**Date**: |
Tue, 14 Sep 2010 14:29:30 -0400 |

**User-agent**: |
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On 09/14/2010 01:33 PM, Fotios Kasolis wrote:

If i recall correctly that was asked time ago! Given an analytic function
f:R->R you can get an approximation of the coefficients of the maclaurin
polynomial by a function like

...

This will not work for singular functions. For instance, it ll return Nans if
your function is f(x) = 1/(1-x) and garbage if there is a singularity. An
example is

`I think this algorithm must have limited convergence radius. Your
``example works to around 1:
`
p = maclaurin (@(x) exp(sin (x)), 10);
x=0:0.01:2;plot (x, exp(sin(x)),x,pv = polyval (p, x))
a plain sin(x) seems to be valid to at least two or so:
p = maclaurin (@(x) (sin (x)), 10);
x=0:0.01:4;plot (x, (sin(x)),x,pv = polyval (p, x))