RE: function assignment to list of functions

• To: mathgroup at smc.vnet.net
• Subject: [mg33725] RE: [mg33720] function assignment to list of functions
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Wed, 10 Apr 2002 00:49:06 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> -----Original Message-----
> From: Mark Morrissey [mailto:mmorriss at sbcglobal.net]
To: mathgroup at smc.vnet.net
> Sent: Tuesday, April 09, 2002 7:04 AM
> Subject: [mg33725] [mg33720] [mg33720] function assignment to list of functions
>
>
>
> 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.
>
> Any ideas??
>
>
> Regards - Mark
> Mark Morrissey
> Unv of Oklahoma
> Norman, Oklahoma 73026
>

Mark,

I do not know what you want to achieve, in general I'd avoid doing that,
because:

(1) you'll loose all predefined transformation rules and simplifications
associated with the Hermite Polynomes, and

(2) you'll also loose the programmed, optimized numerical function
evaluation for them.

In[1]:= (ff = Table[HermiteH[n, z], {n, 0, 10}]) // TableForm
Out[1]//TableForm=
1
2*z
-2 + 4*z^2
-12*z + 8*z^3
12 - 48*z^2 + 16*z^4
120*z - 160*z^3 + 32*z^5
-120 + 720*z^2 - 480*z^4 + 64*z^6
-1680*z + 3360*z^3 - 1344*z^5 + 128*z^7
1680 - 13440*z^2 + 13440*z^4 - 3584*z^6 + 256*z^8
30240*z - 80640*z^3 + 48384*z^5 - 9216*z^7 + 512*z^9
-30240 + 302400*z^2 - 403200*z^4 + 161280*z^6 - 23040*z^8 + 1024*z^10

In[2]:=
(myHerms[#2, z_] := #1) & @@@ Transpose[{ff, Range[Length[ff]] - 1}];

In[3]:= myHerms[5, x]
Out[3]= 120*x - 160*x^3 + 32*x^5

Hope that helps

--
Hartmut Wolf

```

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