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MathGroup Archive 1998

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Re: Help with evaluation of infinite summation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14081] Re: Help with evaluation of infinite summation
  • From: John Baron <johnb at nova.stanford.edu>
  • Date: Tue, 22 Sep 1998 03:25:11 -0400
  • Organization: Center for Radar Astronomy, Stanford University, California USA
  • References: <6tvo8k$1su@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

John Baron <johnb at nova.stanford.edu> writes:

>I have a power series of the form

>	f[x_] = Sum[c[m] x^m, {m, 0, Infinity}]

>which I would like to evaluate over a fairly large range of x.

> <snip>

Just a little more information to add here...

I'm using Sum[] (actually, NSum[]) so that Mathematica can decide when
enough terms have been added, rather than doing that myself. What I had
pictured was Mathematica computing the first NSumTerms terms (default
is 15), adding another NSumExtraTerms terms (default is 12), checking
to see whether the sum has suitably converged, and if not, continue
summing terms until the desired PrecisionGoal is reached.

However, he method which Mathematica chooses to estimate the result, the
Wynn epsilon method, immediately jumps to a very large value for m,
around 90000.  Given the recurrence relation among the series
coefficients, it's no surprise that the default recursion depth is
exceeded very quickly.  And, to my knowledge, the recurrence relation
can't be solved to find c[m] explicitly.  I tried changing the default
method to Integrate, but apparently that doesn't work with my
particular problem formulation.

So I guess my question now would be, is there any way to let Mathematica
handle this?  Or would I be better off just writing the function in the
same way it would appear in C or Fortran code?

Thanks,

John
-- 
__________________________________________________________________ John
Baron         johnb at nova.stanford.edu          (650) 723-3669 Center
for Radar Astronomy        http://nova.stanford.edu/~johnb/


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