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MathGroup Archive 2002

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Re: function assignment to list of functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33706] Re: [mg33720] function assignment to list of functions
  • From: BobHanlon at aol.com
  • Date: Tue, 9 Apr 2002 01:02:36 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 4/8/02 4:20:10 AM, mmorriss at sbcglobal.net writes:

>Hi Folks - I have an alternative form of the set Hermite polynomials I'd
>
>like to use.  They are defined differently than the mathematica function
>
>HermiteH.  Unfortunately, the recursive generating function takes way 
>too long.  I can generate a list of these functions using the different
>
>order derrivatives of the gaussian PDF (that's how they're defined):
>
>{1, -x, -1 + x^2, -x(-3 + x^2) .... }
>
>
>But I don't seem to be able to assign each function to H[x_,i_]:=   
>where i is the index from 0 to the number of functions in the list.
>

H1[x_, i_Integer] :=
 
    Module[{v},
 
      D[Exp[-v^2/2], {v,i}] /.
 
        {Exp[-v^2/2]->1, v->x}];

Table[H1[x,i], {i,0,5}]

{1, -x, x^2 - 1, 3*x - x^3, x^4 - 6*x^2 + 3, -x^5 + 10*x^3 - 15*x}

H2[x_, i_Integer] :=
 
    Module[{v},
 
      Nest[D[#,v]&, Exp[-v^2/2], i] /.
 
        {Exp[-v^2/2]->1, v->x}];

Table[H1[x,i], {i,0,5}]==Table[H2[x,i], {i,0,5}]

True

Table[H1[2,i], {i,0,5}]==Table[H2[2,i], {i,0,5}]

True

Bob Hanlon
Chantilly, VA  USA


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