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how to "dynamically" define such a function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg25644] how to "dynamically" define such a function
*From*: "Zhu X. P." <xpzhu at red.semi.ac.cn>
*Date*: Wed, 18 Oct 2000 02:52:20 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
hello all,
I want to define a function like this:
F[x]=
f[x]=f[m][x] x>L[m],
f[x]=f[m-1][x] L[m-1]<x<L[m],
.... ...
f[x]=f[1][x] L[1]<x<L[2],
f[x]=f[0][x] x<L[1]
"Dynamically define" means "m" is not a fixed number. When m, as well as
L[i] and f[i][x] (i =,1,...,m), is given, F[x] is defined.
I define F[x] as below:
F[x_] =
Module[{n, w},
w[x_, 0] = f[0][x];
w[x_, n_] = If[x > L[n], f[n][x], w[x, n - 1]];
w[x, m]
];
I think this method is not very good. Are there some better ways to
define such a function?
ps. I want to integrate this function F[x]:
Integrate[F[x], {x,a,b}]
when a>L[m], no problem. But when a<L[m] Mathematica tell me like this:
In[48]:=Integrate[F[x], {x, .2, 10}]
Out[48]:=\!\(\[Integral]\_0.2`\%21 If[x > 0.9000000000000001`,
\(f[7]\)[x - L[7 - 1]],
w$52[x, 7 - 1]] \[DifferentialD]x\)
where m=7, 0.9 is the value of L[7]. Who can tell me why this happened?
thank you!
Zhu X. P.
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