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Topic: integrating dirac delta over the real ine when its argument has no
solution on the real line

Replies: 3   Last Post: Apr 13, 2014 10:34 AM

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Nasser Abbasi

Posts: 5,660
Registered: 2/7/05
integrating dirac delta over the real ine when its argument has no
solution on the real line

Posted: Apr 2, 2014 3:25 PM
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What should CAS do when asked to integrate a dirac delta
over the real line when its argument is never zero on
the real line?

There is no solution for 2-cos(t)=0 on real line.

Maple 18:
int( Dirac(2-cos(t)),t=-infinity..infinity);
=========> unevaluated

Mathematica 9.01
Integrate[DiracDelta[2 - Cos[t]], {t, -Infinity, Infinity}]
=======> 0

What does your CAS produce? Another different behavior

Maple:
int( Dirac(I*t),t=-infinity..infinity);
======> 1

and no Mathematica's turn to return unevaluated answer

Integrate[DiracDelta[I t], {t, -Infinity, Infinity}]
=====> remains unevaluated


--Nasser



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