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Re: adding assumptions to Integrate

• To: mathgroup at smc.vnet.net
• Subject: [mg69649] Re: [mg69630] adding assumptions to Integrate
• From: Andrey <newsgroup at gorodok.net>
• Date: Tue, 19 Sep 2006 05:45:10 -0400 (EDT)
• References: <200609180246.WAA09330@smc.vnet.net>
• Reply-to: Andrey <newsgroup at gorodok.net>

> 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