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Re: Re: Log(ln) Function + 2 Parameters + Greater

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89309] Re: [mg89298] Re: Log(ln) Function + 2 Parameters + Greater
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 5 Jun 2008 00:43:00 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <g22tp5$ikl$1@smc.vnet.net> <g237c4$q2n$1@smc.vnet.net> <200806040937.FAA18315@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

f[a_,x_] is a function with two arguments, the first of which is being 
regarded as a "parameter".

f[a_] is a function with one argument, whose value for a given "a" is a 
function to which you can input a value of x.  So the construct 
f[a_][x_] captures more precisely the idea of a family of functions 
parameterized by parameter "a".


Jerry wrote:
> Sir, I have never seen a function definition in the form you 
> give:
> f[a_][x_] := x (a + Log[x])^2
> 
> After a bit of playing with it, I don't see the difference 
> between this and
> 
> f[a_,x_] := x (a + Log[x])^2
> 
> I really don't know how to search in help for this f[a_][x_] 
> form. Can you tell me if there is any essential difference?
> 
> Thank you.
> 
> 
> David Park wrote:
>> First, define your f function with a as a parameter.
>>
>> f[a_][x_] := x (a + Log[x])^2
>>
>> Mathematica can't make a plot unless it knows values for a. Of course, it 
>> won't plot any results for x < 0 and I'm not certain if you actually meant x 
>>  > 0 rather than a > 0. In any case, you can use any real domain for a. Here 
>> is a plot for a specific value of a.
>>
>> Plot[f[2][x], {x, -5, 5},
>>  AxesLabel -> {x, f}]
>>
>> You can look at an extended a domain by using Plot3D.
>>
>> Plot3D[f[a][x], {a, -5, 5}, {x, 0, 5},
>>  PlotRange -> All,
>>  AxesLabel -> {a, x, f}]
>>
>> Another approach is to use a Manipulate statement with a controlled by a 
>> slider.
>>
>> Manipulate[
>>  Plot[f[a][x], {x, 0, 5},
>>   PlotRange -> {0, 250},
>>   AxesLabel -> {x, f}],
>>  Style[Row[{HoldForm[f["a"][x]] == f["a"][x]}], 16],
>>  Delimiter,
>>  {a, -5, 5, Appearance -> "Labeled"}]
>>
>>
>>
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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