       Re: Alternating sums of large numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg91909] Re: Alternating sums of large numbers
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Fri, 12 Sep 2008 05:29:12 -0400 (EDT)

```On 9/11/08 at 6:14 AM, mikhail.lemeshko at gmail.com (Mikhail Lemeshko)
wrote:

>I'm using a Mathematica 6, and I've faced with the following
>problem. Here is a copy of my Mathematica notebook:

>--------------------------------------------------------

>NN = 69.5;

>n = 7;

>coeff = (Gamma[2*NN - n + 1]*(2*NN - 2*n))/n!;
>
>f[z_] := Sum[((-1)^(\[Mu] + \[Nu])*Binomial[n, \[Mu]]*Binomial[n, \
>[Nu]]*Gamma[2*NN - 2*n + \[Mu] + \[Nu], z])/(Gamma[2*NN - 2*n +
>\[Mu] + 1]*Gamma[2*NN - 2*n + \[Nu] + 1]), {\[Mu],0, n}, {\[Nu], 0,
>n}];

>Plot[coeff*f[z], {z, 0, 100}]

>--------------------------------------------------------

>As you can see, I want to calculate a double alternating sum,
>consisting of large terms (products of Gamma-functions and binomial
>coefficients). Then I want to plot the result, in dependence on
>parameter z, which takes part in the summation as an argument of the
>incomplete Gamma-function, Gamma[2*NN - 2*n + \[Mu] + \[Nu], z].

<snip>

>A suppose that this error is caused by the huge numbers with
>alternating signs, contributing to the summation - probably there
>are some mistakes introduced by numerical evaluation.

This is exactly the issue when machine precision numbers are
used. Change NN to an exact number, i.e., NN = 69+1/2 then try.

```

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