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MathGroup Archive 2005

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Re: Re[2]: Re: Numerical accuracy of Hypergeometric2F1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55776] Re: Re[2]: [mg55743] Re: Numerical accuracy of Hypergeometric2F1
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 6 Apr 2005 03:11:04 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

Integrate[x^100/(x+2),{x,0,1}]

-(1317479497632370191204744890981021191757330191571416507401
36152126531/
    256324908932766460163727238732765821900) - 
1267650600228229401496703205376*Log[2] + 
  1267650600228229401496703205376*Log[3]

N[%]

2.81474976710656*^14

Need slightly higher precision

N[%%,20]

0.00331118591352665013637705575274490534`20.000000000000004

NIntegrate[x^100/(x+2),{x,0,1}]

0.003311185913526502


Bob Hanlon

> 
> From: Janos TOTH <jtoth at helka.iif.hu>
To: mathgroup at smc.vnet.net
> Date: 2005/04/05 Tue AM 07:27:22 EDT
> CC: mathgroup at smc.vnet.net
> Subject: [mg55776] Re[2]: [mg55743] Re: Numerical accuracy of Hypergeometric2F1
> 
> Hello Bob,
> 
> I am sorry, I have mistyped something,
> but I am interested in the integral on
> [0,1] and _not_ on [0,2]!
> 
> Thank you for your quick check.
> 
> Janos
> 
> Tuesday, April 5, 2005, 12:39:10 PM, you wrote:
> 
> BH> Works on my version
> 
> BH> $Version
> 
> BH> 5.1 for Mac OS X (January 27, 2005)
> 
> BH> Integrate[x^100/(x+2),{x,0,2}]
> 
> BH> 
-(9503343334714997237896336168082647022052771377490530168503
> BH> 53071587328/
> BH>     1089380862964257455695840764614254743075) - 
> BH> 1267650600228229401496703205376*Log[2] + 
> BH>   1267650600228229401496703205376*Log[4]
> 
> BH> %//N
> 
> BH> 6.306563320381821*^27
> 
> BH> NIntegrate[x^100/(x+2),{x,0,2}]
> 
> BH> 6.306563320381638*^27
> 
> 
> BH> Bob Hanlon
> 
> >> 
> >> From: "janos" <jtoth at helka.iif.hu>
To: mathgroup at smc.vnet.net
> >> Date: 2005/04/05 Tue AM 03:21:13 EDT
> >> To: mathgroup at smc.vnet.net
> >> Subject: [mg55776] [mg55743] Re: Numerical accuracy of Hypergeometric2F1
> >> 
> >> I wanted to calculate Integrate[x^100/(x+2),{x,0,2}] and even the sign
> >> of the result is just negatvie. The reason is the same as above: 
Mathematica 
> >> calculates the integral symbolically, using a hypergeometric function,
> >> then (s)he is unable to numerically evaluate it.
> >> I got the good result if I used NIntegrate.
> >> Janos Toth
> >> Dept Math Anal
> >> Budapest Univ Technol Ecol.
> >> 
> >> 
> 
> 
> 
> 
> Best regards,
>  Janos                            mailto:jtoth at helka.iif.hu
> Tel. (home): 36-1-242-0640
> Tel. (office): 36-1-463-2314
> or  36-1-463-2475
> Fax: 36-1-463-3172
> Homepage: www.math.bme.hu/~jtoth
> 
> 


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