| Author |
Comment/Response |
Michael
|
 12/11/12 07:01am
The problem might be a typo: Should be BesselJ instead of Besselj.
By default, computation time is unconstrained. (You can constrain it, if you should ever want to, with TimeConstrained.)
For your first integral I got
In[2]:= Integrate[
k^2*Exp[I k h]*BesselJ[0, k g], {k, 0, \[Infinity]}] // Timing
Out[2]= {49.125881,
ConditionalExpression[(
I Sqrt[1 - g^2/h^2] h (g^2 + 2 h^2))/(g^2 - h^2)^3,
Abs[Im[g]] < Im[h]]}
For the second, Mathematica did not come up with an answer, either with or without the assumptions I stuck in.
In[8]:= Block[{$Assumptions =
h \[Element] Reals && 0 < k1 < k2 && g \[Element] Reals},
Integrate[k^2*Exp[I k h]*BesselJ[0, k g], {k, k1, k2}]
] // Timing
Out[8]= {15.322764, \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(k1\), \(k2\)]\(\(
\*SuperscriptBox[\(E\), \(I\ h\ k\)]\
\*SuperscriptBox[\(k\), \(2\)]\ BesselJ[0,
g\ k]\) \[DifferentialD]k\)\)}
(When Mathematica returns the integral unevaluated, it means it could not find an answer in terms of standard functions.)
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