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Dirac delta function how did they prove this?

  1. Jan 27, 2013 #1
    Hi all,

    I'm familiar with the fact that the dirac delta function (when defined within an integral is even)

    Meaning delta(x)= delta(-x) on the interval -a to b when integral signs are present

    I want to prove this this relationship but I don't know how to do it other than with a limit maybe

    Book said they proved it using a change of variables and changing limits of integration but I can't see how they proved it? Does anyone know how?
     
  2. jcsd
  3. Jan 27, 2013 #2

    HallsofIvy

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    What you have written is pretty much meaningless. The "Dirac Delta function" is not a function at all. It is a "distribution" or "generalized function" which means it is applied to functions, not numbers as are ordinary functions. In particular, that means that we do not define either [itex]\delta(x)[/itex] or [itex]\delta(-x)[/itex] for specific values of x. What is true is that [itex]\delta[/itex] applied to an odd function is 0.
     
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