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Integral of products of BesselJ

Posted 10 years ago

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 http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/21/02/02/ or http://dlmf.nist.gov/1.17#E13 1.17.13

This is in Mathematica 9.0.1.0. Is this incomplete? Is it fixed in the latest Mathematica

POSTED BY: Mark Shattuck

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

POSTED BY: Sean Clarke
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