Groups > comp.soft-sys.math.maple > #801

Re: Approximating the sum of a series

Newsgroups	comp.soft-sys.math.maple
Date	2013-07-23 07:01 -0700
References	<96195d9d-cdfd-4850-a75b-05e368c4db94@googlegroups.com>
Message-ID	<51a26cdf-75fd-41b0-8c5d-df7b25abf196@googlegroups.com> (permalink)
Subject	Re: Approximating the sum of a series
From	acer <maple@rogers.com>

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On Tuesday, July 23, 2013 3:48:22 AM UTC-4, mma...@personal.ro wrote:
> I want to compute
> 
> evalf(s(0,infinity));
> 
> 
> 
> where
> 
> s:=(a,b)->Sum(exp(-n^2/10000),n=a..b);
> 
> 
> 
> and Maple refuses. It (probably) declares the series divergent.
> 
> Maple accepts to approximate s(1000,infinity).  
> 
> It is < 10^(-42) so, s(0,1000) gives the answer but
> 
> the question is: how could Maple be convinced to compute directly
> 
> evalf(s(0,infinity))?



> kernelopts(version);

            Maple 17.00, X86 64 LINUX, Feb 21 2013, Build ID 813473

> s:=(a,b)->Sum(exp(-n^2/10000),n=a..b): 

> evalf( s(0,9) + s(10,infinity) );     

                                  89.12269254


It appears to be equal to the following (an equivalent of which which Mathematica gave, but which I have not so far obtained directly in Maple),

> U:=1/2*(1+JacobiTheta3(0,exp(-1/10000))):

> evalf[20](U);

                             89.122692545275801400

> expand(simplify(convert(U,Sum)));

                              /infinity             \
                              | -----            2  |
                              |  \            _k1   |
                          1 + |   )     exp(- -----)|
                              |  /            10000 |
                              | -----               |
                              \_k1 = 1              /

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Approximating the sum of a series mmatica@personal.ro - 2013-07-23 00:48 -0700
  Re: Approximating the sum of a series "Nasser M. Abbasi" <nma@12000.org> - 2013-07-23 07:17 -0500
  Re: Approximating the sum of a series acer <maple@rogers.com> - 2013-07-23 07:01 -0700
    Re: Approximating the sum of a series Axel Vogt <&noreply@axelvogt.de> - 2013-07-23 18:57 +0200
  Re: Approximating the sum of a series mmatica@personal.ro - 2013-07-23 12:13 -0700
  Re: Approximating the sum of a series mmatica@personal.ro - 2013-07-23 12:29 -0700
    Re: Approximating the sum of a series Axel Vogt <&noreply@axelvogt.de> - 2013-07-23 22:11 +0200
      Re: Approximating the sum of a series mmatica@personal.ro - 2013-07-23 14:08 -0700
        Re: Approximating the sum of a series Axel Vogt <&noreply@axelvogt.de> - 2013-07-28 19:40 +0200
        Re: Approximating the sum of a series / an Integral Axel Vogt <&noreply@axelvogt.de> - 2013-07-29 22:22 +0200
          Re: Approximating the sum of a series / an Integral Herman Rubin <hrubin@skew.stat.purdue.edu> - 2013-07-30 18:03 +0000
      Re: Approximating the sum of a series Herman Rubin <hrubin@skew.stat.purdue.edu> - 2013-07-25 23:37 +0000
    Re: Approximating the sum of a series acer <maple@rogers.com> - 2013-07-23 14:02 -0700

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