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Re: Integrate returns 0

n a message dated 6/15/2000 1:13:26 AM, felix.klee at writes:

>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}]
>    Sqrt[Pi/2]
>Is this a bug in Mathematica or am I doing something wrong?

This is a bug, the answer should be:

\!\(2\^\(\(-\(1\/2\)\) + n\)\ Gamma[1\/2 + n]\)


Intf[n_?IntegerQ] :=
  \!\(2\^\(\(-\(1\/2\)\) + n\)\ Gamma[1\/2 + n]\)

compare the output of

Table[Intf[n], {n, 0, 10}]

with Bob Hanlon's answer in [mg23915]


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