Re: Defining Operators

• To: mathgroup at smc.vnet.net
• Subject: [mg44803] Re: Defining Operators
• From: Roberto Brambilla <rlbrambilla at cesi.it>
• Date: Thu, 27 Nov 2003 11:38:29 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi  Guthery, try this

IntegrationOperator[f_,s_]:= Module[{func},
func=Function@@{f /.s -> #1};
Integrate[func[s],{s,0,1}]

where s is the integration variable, that, of course, must be present in
the arguments of the function to be integrate.

Example

g[x_,y_,z_]:=x Cos[w y] Tanh[m z]

f[[t_,y_]:=Evaluate[IntegrationOperator[g[x,t,y],x]
h[x_,q_]:=Evaluate[IntegrationOperator[g[x,t,q],t]
r[x1_,x2_]:=Evaluate[IntegrationOperator[g[x1,x2,s],s]

?f
f[t_,y_]:=1/2 Cos[w t] Tanh[m y]
?h
h[x_]:= x Sin[w]Tanh[mq]/w
?t
r[x1_,x2_]:=x1 Cos[w x2]Log[Cosh[m]]/m

You can also add a kernel to integrals , as in integral transforms

Kern[x_,y_]:= Exp[ - x y]

myTransform[f_,x_,p_]:= Module[{func},
func=Function@@{f /.x-> #1};
Integrate[func[x]Kern[x,p],{x,0,Infinity},GenerateConditions->False]]

Example:

myTransform[BesselJ[0,w y],y,z]
1/Sqrt[w^2+z^2]

Bye Rob

Roberto Brambilla
CESI
Via Rubattino 54
20134 Milano
tel +39.02.2125.5875
fax +39.02.2125.5492
rlbrambilla at cesi.it

```

• Prev by Date: Re: change of a coefficient in a polynomial
• Next by Date: Re: Table format gets lost while write to outputfile?
• Previous by thread: Re: Defining Operators
• Next by thread: How to get single letters bold instead italic