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Re: Approximating the sum of a series

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From	Axel Vogt <&noreply@axelvogt.de>
Newsgroups	comp.soft-sys.math.maple
Subject	Re: Approximating the sum of a series
Date	Tue, 23 Jul 2013 18:57:13 +0200
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On 23.07.2013 16:01, acer wrote:
> 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);
...
...
> 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              /

Ignoring the usual conditions and using Abel-Plana (so it
has to be justified) I get 1/2 + sqrt(k*Pi)/2, 0 < k=10000

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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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