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