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Subject: Re: Hermite polynomials with complex parameters.
Date: Fri, 2 Mar 2012 18:15:17 +0000 (UTC)
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"Nasser M. Abbasi" <nma@12000.org> wrote in message <jipvcj$ro$1@speranza.aioe.org>...
> The above only gives you one numerical value. Not a polynomial,
> which is what you asked for:
> In[7]:= HermiteH[1 + I, 0.5]
> Out[7]= 1.9951895074974817 - 0.29935560945022155*I
> I thought you wanted a Hermite polynomial, as in
> In[8]:= HermiteH[5, x]
> Out[8]= 120*x - 160*x^3 + 32*x^5
> which only works for non-negative integers.
> If I type
> HermiteH[1 + I, x]
> then Mathematica does not do anything with it.
- - - - - - - - - -
  Hi Nasser.  I see nothing contradictory in the various results you get with HermiteH.  HermiteH(n,z) when n is a positive integer is in fact a polynomial function of z which can be given a specific polynomial coefficient format rather than simply a value.  However when n is otherwise, there is no way that Mathematica can express what function of z it is, so as you say, it "does not do anything with it".  On the other hand if you give a specific value for z, then HermiteH can return with the corresponding function value for that z which it apparently does in every case, hence your single result for HermiteH[1+I,0.5].

  When Xiang originally asked "how to simulate hermite polynomials" it was presumably a minor misnomer which was later corrected by saying "For general 'n', its actually hermite function."

Roger Stafford