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