Re: Function-type arguments in function definition

*To*: mathgroup at smc.vnet.net*Subject*: [mg44301] Re: Function-type arguments in function definition*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 5 Nov 2003 10:00:25 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <bo7o3k$aep$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de*Sender*: owner-wri-mathgroup at wolfram.com

Hi, and conv[f_, g_][x_] := Module[{y}, Integrate[f[y]*g[x - y], {y, a, b}]] conv[#^2 &, Exp[-#] &][x] does not what you whant ? Regards Jens Carsten Reckord wrote: > > Hi, > > I'm pretty new to Mathematica so please excuse me if this is kind of a silly > question (though I couldn't find any answer after a full day of searching). > I'm trying to define functions that take other functions as arguments and > need those functions' arguments in their own definition. An example would be > the definition of convolution: > > h(x)=f(x)*g(x) is defined as Integral over f(y)g(x-y) with respect to y. > > As you can see it is important in the definition of convolution to treat the > arguments f and g as functions because the definition makes use of their > arguments. > I've seen this done in Mathematica as > > convolute[f_,g_,x_]:=Integrate[f[y]*g[x-y],{y,-inf,inf}] > > but that's not exactly what I'm looking for because I can only use function > names as arguments to convolute[...], not arbitrary expressions in x. So I > can't for example use it for the convolution f(s(x))*g(t(x)) without > defining intermediate functions for f(s(x)) and g(t(x))... > > So, my question is if there is any way to define such a function that can > make use of its arguments being functions and yet supports arbitrary > expressions as its arguments? > > Thanks, > Carsten