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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