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MathGroup Archive 2000

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Re: Integrate returns 0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23916] Re: Integrate returns 0
  • From: "Kevin J. McCann" <Kevin.McCann at jhuapl.edu>
  • Date: Fri, 16 Jun 2000 00:56:56 -0400 (EDT)
  • Organization: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA
  • References: <8i9pj8$2hq@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Probably not a bug, but how Mathematica treats the derivative. I suspect that Mathematica
does not evaluate the derivative within the integral.  It would require that
Mathematica first find a general closed-form expression for the derivative, and then
evaluate that. BTW, the general answer is

(2n)!/(2^n n!)*Sqrt[Pi/2]

for integer n. Looks like it has something to do with Legendre polynomials.

Kevin

Felix E. Klee <felix.klee at inka.de> wrote in message
news:8i9pj8$2hq at smc.vnet.net...
> Hi,
>
> when I define the function
>     f[x_,n_]:=D[Exp[-x^2],{x,n}]^2
> and execute
>     Integrate[f[x,n],{x,-Infinity,Infinity}]
> the result is
>     0
>
> However this is not correct for all parameters n since
>     Integrate[f[x,1],{x,-Infinity,Infinity}]
> returns
>     Sqrt[Pi/2]
>
> Is this a bug in Mathematica or am I doing something wrong?
>
> TIA,
>
> Felix
>




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