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 ÎÎ³Ï?Î±Ï?Îµ: > > 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