shattuck
September 17, 2014, 5:45pm
1
This answer seems incomplete
In[36]:= Integrate[a t BesselJ[0, a t] BesselJ[0, b t], {t, 0, Infinity}]
Out[36]= ConditionalExpression[0, b >= 0 && Re[a] > b && a == Re[a]]
I think the answer should be DiracDelta[a-b]
see Bessel function of the first kind: Integration (subsection 21/02/02) DLMF: §1.17 Integral and Series Representations of the Dirac Delta ‣ Topics of Discussion ‣ Chapter 1 Algebraic and Analytic Methods 1.17.13
This is in Mathematica 9.0.1.0. Is this incomplete? Is it fixed in the latest Mathematica
seanc
September 17, 2014, 9:32pm
2
What you’re seeing here is a common “gotcha” of symbolic computing. Integrals of orthogonal functions are a common case where Integrate behaves differently than how we normally write out math.
In short, Integrate gives generic results (http://reference.wolfram.com/language/tutorial/GenericAndNonGenericCases.html)
Here is an example from Stackexchange of a similar integral which has a very good answer from someone way more knowledgable about this than me:http://mathematica.stackexchange.com/questions/19833/usage-of-assuming-for-integration