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

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  • 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
>>
>>




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