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 >