       Re: integral tranform definition

• To: mathgroup at smc.vnet.net
• Subject: [mg33154] Re: integral tranform definition
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 6 Mar 2002 01:55:28 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <a61uf4\$gin\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

can you be so kind and post correct Mathematica syntax if you write
mathematics ? You can't avoid to use function but
you can define pure functions on fly with:

Kern[n_, y_, x_] = Sin[n x y]

MyTransf[n_, func_, y_] :=
Integrate[Kern[n, y, x] func[x], {x, 0, 2 Pi}] // FullSimplify

g[t_, m_] := MyTransf[m, Cos[5*#] &, t]

m = 4; g[z, m]

m = 2;
MyTransf[m, g[#, 4] &, t]

Regards
Jens

Roberto Brambilla wrote:
>
> Hi all math-friends,
>
> I have a little problem in integral transform definition.
> I want to define the following integral transform depending on a parameter n
>
> g(y,n)=integral[K(n,y,x)f(x)dx] (a<=x<=b)
>
> where, for example, Kern(n,y,x)=sin(n x y)  in (0-2Pi) square.
>
> So a I build the function
>
> MyTransf[n_, func_, y_] :=  Integrate[Kern[n, y, x] func[x],
>                             {x, 0, 2 Pi}] // FullSimplify
>
> and try it
>
> test1[x_]:=Cos[5 x]
> g[t_, m_] := Evaluate[MyTransf[m, test1, t]]
>
> m=4; g[z,m]
> (out)  8 z (Sin[4 pi z])^2/(16 z2-25)
>
> So far so good. Now I want to apply MyTransf again to this result, changing
> the parameter.
> I have to define an intermediate function without parameters and sigle
> variable
>
> test2[x_]:=g[x,4]
>
> and then
>
> m=2;
> Evaluate[MyTransf[m, test2, t]]
> (out) 1/16((-CosIntegral[.................etc.........
>
>
> My problem is to avoid the definition of the intermediate function.
> How can define MyTrans so that I can write simply
>
> MyTransf[n, func[m1,m2,...,x], y]
>
> i.e a definition where I can use funcions with explicited parameter(s)
> m1,m2..,
> the name of the input variable (here x) and the name of the output variable
> (here y)?
> Having this definition, I could write (my final wish)
>
> MyTransf[n2, MyTransf[n1, f1[m1,x], y], z]
>
> and then find for each n1 the vale of n2 (if exist) for which this double
> transform
> correspond to other transform, i.e. I want to test if these transforms act
> like a group.
> Rob.
>
> Roberto Brambilla
> CESI
> Via Rubattino 54
> 20134 Milano
> tel +39.02.2125.5875
> fax +39.02.2125.5492
> rlbrambilla at cesi.it

```

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