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MathGroup Archive 2007

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Re: Integrate[s^s(1-s)^(1-s)Sin[Pi s],{s,0,1}]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76201] Re: Integrate[s^s(1-s)^(1-s)Sin[Pi s],{s,0,1}]
  • From: Nacho <ncc1701zzz at gmail.com>
  • Date: Thu, 17 May 2007 06:14:42 -0400 (EDT)
  • References: <f2bs3m$ga6$1@smc.vnet.net>

On May 15, 10:47 am, janos <janostothmeis... at gmail.com> wrote:
> Any idea to calculate this integral (symbolically) or reformulate it
> using some special functions?
>
> Thanks, Janos


I don't know if Mathematica can calculate it simbolically, but if you
calculate it numerically with enough precision, you can use the
Plouffe's Inverter ( http://pi.lacim.uqam.ca/eng/ ) to check that it
is Pi*E/24 (or at least, very very close to)

NIntegrate[s^s(1-s)^(1-s)Sin[Pi s],{s,0,1}, WorkingPrecision->40]
0.355822259278065294394314619564

N[Pi*E/24,30]
0.355822259278065294394314619564


Regards.



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