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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122814] large integration result for simple problem: 1/x,, also BesselJ
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Fri, 11 Nov 2011 04:55:15 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

(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




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