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From: TamuKevin on 11 Apr 2010 11:24
My problem says to find the Maclaurian series of "f" and its radius on convergence. Graph "f" and its first few Taylor Polynomials on the same screen.

f= sqrt(1 +x)

How do I find a mac series on Matlab? Thanks
From: Roger Stafford on 11 Apr 2010 20:30
TamuKevin <custom_audio_11(a)yahoo.com> wrote in message <222674914.546754.1271013904886.JavaMail.root(a)gallium.mathforum.org>...
> My problem says to find the Maclaurian series of "f" and its radius on convergence. Graph "f" and its first few Taylor Polynomials on the same screen.
>
> f= sqrt(1 +x)
>
> How do I find a mac series on Matlab? Thanks

The Maclaurin series is just a Taylor series expanded about x = 0. Read the description of matlab's 'taylor' function in the symbolic toolbox very carefully and you can do everything asked of you quite easily, except possibly determine the radius of convergence. For that to be done rigorously you would need to have the general formula for the n-th coefficient of the series and some knowledge about power series convergence. This general formula can be obtained from the binomial theorem applied to fractional powers. Either that or know something about analytic (complex) function theory. It is this latter field which gives significance to the word 'radius' in "radius of convergence".

Roger Stafford
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