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/