Re: large integration result for simple problem: 1/x,, also BesselJ

*To*: mathgroup at smc.vnet.net*Subject*: [mg122858] Re: large integration result for simple problem: 1/x,, also BesselJ*From*: Richard Fateman <fateman at eecs.berkeley.edu>*Date*: Sat, 12 Nov 2011 07:36:33 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On 11/11/2011 7:46 AM, Andrzej Kozlowski wrote: > Mathematica 8 gives: > > Integrate[BesselJ[n, b*x], {x, 0, Infinity}, Assumptions -> {Re[n]> -1, Im[b] == 0}] > > Sign[b]^n/Abs[b] Mathematica 7 gives the same answer with those assumptions. What's your point? In my command, where I leave off the Im[b]==0 , I got an answer that includes.. If [ Abs[Im[b]] == 0, b^(-2 + n) (b^2)^(1/2 - n/2), ..... To me, Abs[Im[b]] == 0 means the same as Im[b]==0, so why does the answer say Abs[...]==0? Why is the user required to feed back into the Integrate program the condition it derives, as an Assumption, in order to get a simplified result? Does Mathematica 8 return b^(-2 + n) (b^2)^(1/2 - n/2) ? Does Mathematica 8 do any better for integrating 1/x ? (Sorry, UC Berkeley seems to have let their upgrade lapse). Wolfram Alpha times out on this. It also times out on the Bessel integral. RJF > > > > Note the additional assumption on b. Without it the result is clearly not true. > > Andrzej Kozlowski > > > On 11 Nov 2011, at 10:55, Richard Fateman wrote: > >> (at least in Mathematica 7.0) >> >> try >> >> Integrate[1/x,{x,a,b}] >> >> Also >> >> Integrate[BesselJ[n, b*x], {x, 0, Infinity}, Assumptions -> Re[n]> -1 ] >> >> which returns an expression including this .... >> >> b^(-2 + n) (b^2)^(1/2 - n/2) >> >> which should be possible to simplify. For example, for b>0, the >> expression is 1/b. >> >> maybe 1/b * If[b>0, 1 , -(-1)^n] or so. >> >> I've been playing with integration of expressions involving Bessel >> functions. Mathematica is sometimes surprising, on both sides of the >> ledger -- (Yes we Can and No we Can't). >> >> >> RJF >> >>