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MathGroup Archive 2006

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Re: Why all the if's the answer

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70823] Re: Why all the if's the answer
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Sat, 28 Oct 2006 23:37:55 -0400 (EDT)
  • References: <ehs31u$oe4$1@smc.vnet.net>

Dear Aaron,

With all these Log and Sqrt and so many parameters around,
I think it is not very reliable to use GenerateConditions->False
(except you want the finite part of the integral that many
times the setting GenerateConditions->False gives or you are sure
that your integral converge in the Riemann sense and you don't want
Mathematica to search for it)

BTW,

Timing[Integrate[(Sin[x]/(1 + x^2)^m)*BesselJ[n, x], {x, 0,
Infinity}]][[1]]
60.266 Second

Timing[Integrate[(Sin[x]/(1 + x^2)^m)*BesselJ[n, x], {x, 0, Infinity},
GenerateConditions -> False]][[1]]
6.281 Second

So, you see the advantage of GenerateConditions->False setting; the
time.
But, see now the drawback;

Integrate[(Cos[x]/x)*Exp[(-s)*x], {x, 0, Infinity}, GenerateConditions
-> False]
(1/2)*(-EulerGamma - Log[1 + 1/s^2] + Log[1/s^2])

Integrate[(Cos[x]/x)*Exp[(-s)*x], {x, 0, Infinity}]
Integrate::idiv: Integral of Cos[x]/x)*Exp[(-s)*x] does not converge on
{0,8}
Cos[x]/x)*Exp[(-s)*x]

Regards
Dimitris


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