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Re: Integrate returns 0
*To*: mathgroup at smc.vnet.net
*Subject*: [mg23915] Re: [mg23888] Integrate returns 0
*From*: BobHanlon at aol.com
*Date*: Fri, 16 Jun 2000 00:56:55 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
In a message dated 6/15/2000 1:13:26 AM, felix.klee at inka.de 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}]
>returns
> Sqrt[Pi/2]
>
>Is this a bug in Mathematica or am I doing something wrong?
>
You need to delay integration until a specific value of n is defined.
f[x_, n_] := D[Exp[-x^2], {x, n}]^2
g[x_, n_Integer] := Integrate[f[x, n] , {x, -Infinity, Infinity}]
Table[g[x, n], {n, 0, 5}]
{Sqrt[Pi/2], Sqrt[Pi/2], 3*Sqrt[Pi/2], 15*Sqrt[Pi/2],
105*Sqrt[Pi/2], 945*Sqrt[Pi/2]}
(Integrate[#, {x, -Infinity, Infinity}] & /@ Table[f[x, n], {n, 0, 5}]) ==
Table[Integrate[f[x, n], {x, -Infinity, Infinity}], {n, 0, 5}] ==
Table[g[x, n], {n, 0, 5}]
True
Bob Hanlon
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