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integration using PSQL algorithm
*To*: mathgroup at smc.vnet.net
*Subject*: [mg52332] integration using PSQL algorithm
*From*: Arturas Acus <acus at itpa.lt>
*Date*: Wed, 24 Nov 2004 02:32:03 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Dear group,
I have some reasons to suspect that some integral may have closed form
in terms of powers of Pi: a+b*Pi+c*Pi^2+d*Pi^3+e*Pi^4 (a,b,c,d,e being
algebraic numbers, probably with a=d=0). Assuming I can calculate the
integral numerically to desired precision, is it possible to verify this
hypothesis. As far as I know, the PSLQ algorithm, which helps to find
algebraic relations between real numbers, can be useful here. The only
(Mathematica related) reference I know is
http://library.wolfram.com/infocenter/MathSource/4263/
, but the example here is too simple.
As for details, the integral in consideration is
integral = (-6*(-1 + a)*(4*Sqrt[7 + a] + Sqrt[2]*(5 + a)*Pi))/((5 +
a)*(7 + a)^(3/2)) -
(24*(-1 + a)*(6 + a)*Log[6 + a - Sqrt[5 + a]*Sqrt[7 + a]])/((5 + a)*(7
+ a))^(3/2)
with a= Cos[4* phi], integrated from 0 to Pi/2 (or to 2 Pi, no matter)
The problems arises from second term.
Mathematica 5.0 can't do it symbolically. How about 5.1?
Sincerely,
--
Arturas Acus <acus at itpa.lt>
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