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

*To*: mathgroup at smc.vnet.net*Subject*: [mg122856] Re: large integration result for simple problem: 1/x,, also BesselJ*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 12 Nov 2011 07:36:11 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111110955.EAA08514@smc.vnet.net>

Mathematica 8 gives: Integrate[BesselJ[n, b*x], {x, 0, Infinity}, Assumptions -> {Re[n] > -1, Im[b] == 0}] Sign[b]^n/Abs[b] 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 > >

**References**:**large integration result for simple problem: 1/x,, also BesselJ***From:*Richard Fateman <fateman@cs.berkeley.edu>