       Re: Howto vonvert a list of functions in a list valued function

• To: mathgroup at smc.vnet.net
• Subject: [mg28300] Re: [mg28253] Howto vonvert a list of functions in a list valued function
• From: "Mark Harder" <harderm at ucs.orst.edu>
• Date: Sat, 7 Apr 2001 03:45:01 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```    I just realized that there is a simpler method  (letting funlist[x]
[[i]]=Sin[x/(2*i) ], for example):

nFunc=10;
Clear[x, f];
f := Table[Sin[#/(2 i) ], {i, nFunc} ] &;

In:=f[x]
f[Pi]

Out=
{Sin[x/2], Sin[x/4], Sin[x/6], Sin[x/8], Sin[x/10], Sin[x/12], Sin[x/14],
Sin[x/16], Sin[x/18], Sin[x/20]}
Out=
{1, 1/Sqrt, 1/2, Sin[Pi/8], 1/4*(-1 + Sqrt), (-1 +
Sqrt)/(2*Sqrt), Sin[Pi/14], Sin[Pi/16],
Sin[Pi/18], Sin[Pi/20]}

-mark harder

-----Original Message-----
From: Mark Harder <harderm at ucs.orst.edu>
To: mathgroup at smc.vnet.net
<mathgroup at smc.vnet.net>
Subject: [mg28300] Re: [mg28253] Howto vonvert a list of functions in a list valued
function

>Thomas,
>    As you have defined it, funlist is only a list of undefined expressions
>f1,f2, etc., i.e. they are *not* functions.  To define a mapping as a list
>of functions numbered as you wish, I would do this with one function
>definition:
>
>In:= Clear[x];
>            nFunc = 10;
>            f[x_] = Table[ToExpression["f" <> ToString[i] <> "[x]" ], {i,
>nFunc} ]
>
>Out= {f1[x], f2[x], f3[x], f4[x], f5[x], f6[x], f7[x], f8[x], f9[x],
>f10[x]}
>
>or, for example,
>In:=  f[x_] = Table[ToExpression["Exp[" <> ToString[i] <> " x]" ], {i,
>nFunc} ]
>                f[a]
>
>Out=
>{E^x, E^(2*x), E^(3*x), E^(4*x), E^(5*x), E^(6*x), E^(7*x), E^(8*x),
>E^(9*x), E^(10*x)}
>Out=
>{E^a, E^(2*a), E^(3*a), E^(4*a), E^(5*a), E^(6*a), E^(7*a), E^(8*a),
>E^(9*a), E^(10*a)}
>
>mark harder
>harderm at ucs.orst.edu
>
>
>-----Original Message-----
>From: Thomas Neff <t.neff at gsi.de>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net <mathgroup at smc.vnet.net>
>Date: Thursday, April 05, 2001 11:11 PM
>Subject: [mg28300] [mg28253] Howto vonvert a list of functions in a list valued
>function
>
>
>>I have a list of functions, say
>>
>>funlist = {f1, f2, f3, ..., fn}
>>
>>I want to construct a function f, so that
>>
>>f[x] gives the list {f1[x], f2[x], f3[x], ... fn[x]}
>>
>>f[x_] = funlist[x] doesn't work ;-(
>>
>>Is there an elegant way to do this in Mathematica ?
>>
>>
>>Thanks
>>
>>Thomas
>>
>>--
>>Thomas Neff
>>Gesellschaft fuer Schwerionenforschung (GSI)
>>Email: t.neff at gsi.de   -   PGP key available
>>WWW:  http://theory.gsi.de/~tneff/tneff.html
>>
>

```

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