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Groups > comp.soft-sys.math.maple > #805
| From | Axel Vogt <&noreply@axelvogt.de> |
|---|---|
| Newsgroups | comp.soft-sys.math.maple |
| Subject | Re: Approximating the sum of a series |
| Date | 2013-07-23 22:11 +0200 |
| Message-ID | <b586ekF9189U1@mid.individual.net> (permalink) |
| References | <96195d9d-cdfd-4850-a75b-05e368c4db94@googlegroups.com> <bb9dfff8-cc30-48fd-8c75-02c2f5c7d10e@googlegroups.com> |
On 23.07.2013 21:29, mmatica@personal.ro wrote: > The problem is not related to the exact sum of the series > but about the possibility to approximate such series (directly) in Maple. > (there should be some flags/options). > > BTW, Borwein & Borwein have proved that > > 1/10^5*sum(exp(-n^2/(10^10)),n=-infinity..infinity) > > = sqrt(Pi) + e > > 0< |e| < 10^(-42000000000) > Ok, I am not Borwein^2 and assuming their result the suggested formula can not be correct (BTW: the assumptions for AbelPlana are not satisfied). For the numerical question I would guess: something similar to slowly convergent integrals happens and Maple's accellerators can not handle it (not even in high precision), exp(-10^5) is too 'close' to one (for larger n).
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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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