integral transform definition

• To: mathgroup at smc.vnet.net
• Subject: [mg33259] integral transform definition
• From: Roberto Brambilla <rlbrambilla at cesi.it>
• Date: Tue, 12 Mar 2002 05:08:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello Jens-Peer, hello all friends

now it is all OK ! Thank you very mutch : it is exactly what I wanted!

Transf[n_, f_, s_, t_] := Module[{trafo, func, w},
func = Function @@ { f /. s -> #1};
trafo = Integrate[Kern[n, t, w] func[w], {w, a, b}]
]

that don't work with explicit variables.
This your improved version is perfecly working

newTransf[n_, f_, s_, t_] := Module[{trafo, func},

func = Function @@ {f /. s -> #1};

trafo = Integrate[Kern[n, s, t] func[s], {s, a, b}]]

is perfecly working.
Now, having defined some function foo[c1,c2,..,x] depending
on some parameters, and a generic kernel  Kern[n,p,q], a<p,q<b,
I can iteratively transform foo without explicit use of pure function,
i.e. with an obvious chain rule

newTransf[n,foo[c1,c2,..,s],s,x]

newTransf[m,
newTransf2[n, foo[c1,c2,..,s]],s,t],t,x]

newTransf[j,
newTransf[m,
newTransf[n,foo[c1,c2..,s],s,t],t,z],z, x]

where the last variable, x, is the lone surviving one - the others, s,t,z
are dummy and changeable.

Best regards Roberto

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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