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Re: adding assumptions to Integrate

• To: mathgroup at smc.vnet.net
• Subject: [mg69659] Re: adding assumptions to Integrate
• From: dimmechan at yahoo.com
• Date: Wed, 20 Sep 2006 02:44:03 -0400 (EDT)
• References: <200609180246.WAA09330@smc.vnet.net><eeoffc$2te$1@smc.vnet.net>

Dear Andrey,
I know that this happen.
I understand that Mathematica need less and less time because it execute
the same integral but all these evaluations are not independent?

Thanks anyway.

Regards

Î?/Î? Andrey έγÏ?αÏ?ε:
> > However I do not understand why exist the big difference in times
> > below.
>
> > Timing[Assuming[Re[m] > 0 && Re[n] > 0, Integrate[BesselJ[n, x]/(1 +
> > x)^m,
> > {x, 0, Infinity}]]][[1]]
> > 39.71900000000001*Second
>
> > Timing[Integrate[BesselJ[n, x]/(1 + x)^m, {x, 0, Infinity}, Assumptions
> ->>
> Re[m] >> 0 && Re[n] > 0]][[1]]
> > 15.859000000000009*Second
>
> > Timing[Block[{$Assumptions = Re[m] > 0 && Re[n] > 0},
> > Integrate[BesselJ[n, x]/(1 + x)^m, {x, 0, Infinity}]]][[1]]
> > 8.734000000000009*Second
>
> > old$Assumptions = $Assumptions;
> > $Assumptions = Re[m] > 0 && Re[n] > 0;
> > Timing[Integrate[BesselJ[n, x]/(1 + x)^m, {x, 0, Infinity}]][[1]]
> > $Assumptions = old$Assumptions; Clear[old$Assumptions]
> > 6.891000000000005*Second
>
> > I will really appreciate any kind of guidance.
>
> > Dimitris Anagnostou
>
> If you will quit kernel after each execution you will see that
> necessary times are almost equal (for me it is 30 sec) (don't forget to
> load kernel by executing something)
> 
> Andrey B.

• References:
  • adding assumptions to Integrate
    • From: dimmechan@yahoo.com