MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


On 11 Nov 2011, at 18:30, Richard Fateman wrote:

> On 11/11/2011 9:16 AM, Andrzej Kozlowski wrote:
>> On 11 Nov 2011, at 18:08, Richard Fateman wrote:
>>
>>> On 11/11/2011 8:38 AM, Andrzej Kozlowski wrote:
>>>> Mathematica 8 returns:
>>>>
>>>>
>>>> Integrate[BesselJ[n, b*x], {x, 0, Infinity},
>>>>  Assumptions ->   {Re[n]>   -1}]
>>>>
>>>>  b^(n - 2)*(b^2)^(1/2 - n/2)
>>>>
>>>> Andrzej Kozlowski
>>> So by your previous note, this answer from version 8.0  is wrong 
since it does not exclude Im[b]==0.
>>> I note that the formula is also wrong unless it somehow excludes 
b==0, when the integral is infinite,
>>> but the formula is indeterminate.
>> I assume you must mean that it is wrong because it does not exclude 
Im[b]!=0 (in other words, a non-real number).
> yes, I mistyped that.  With your correction, the bug is now correctly 
reported.  I assume you agree that it is a bug, and that furthermore the 
response to Integrate[1/x,{x,a,b}]  is miserable.
>


In my opinion it is a bug, albeit a minor one. Mathematica 8 answer to 
the other integral is different form that in v. 7:

Integrate[1/x, {x, a, b}]

ConditionalExpression[Log[b] - Log[a], ((Im[a] >= Im[b] && Re[a]*Im[b] 
<= Im[a]*Re[b]) ||
    (Re[a]*Im[b] >= Im[a]*Re[b] && Im[a] <= Im[b])) && ((Re[a/(b - 
a)] >= 0 && a^2 != a*b) ||
    NotElement[a/(a - b), Reals] || Re[a/(a - b)] >= 1)]

I looks to me like a reasonable answer. ConditionalExpression has now 
replaced If, and it seems to be better integrated with Mathematica's 
Assumptions mechanisms than is the case with If. For example:

Refine[ConditionalExpression[Sqrt[x^2], x > 0]]

ConditionalExpression[x,x>0]

while

Refine[If[x > 0, Sqrt[x^2]]]

If[x>0,Sqrt[x^2]]


Andrzej



  • Prev by Date: Re: large integration result for simple problem: 1/x,, also BesselJ
  • Next by Date: Re: large integration result for simple problem: 1/x,, also BesselJ
  • Previous by thread: Re: large integration result for simple problem: 1/x,, also BesselJ
  • Next by thread: Re: large integration result for simple problem: 1/x,, also BesselJ