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Re: Hermite Polynomials of fractional order

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132121] Re: Hermite Polynomials of fractional order
  • From: enrico.bibbona at gmail.com
  • Date: Sat, 14 Dec 2013 04:03:59 -0500 (EST)
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  • References: <4upfrh$48n@dragonfly.wolfram.com>

On Tuesday, August 13, 1996 9:00:00 AM UTC+2, Vijay Fafat wrote:
> Mathematica gives values for hermite polynomials even when the order
> of the polynomial is a real number. For e.g. HermiteH(0.3,0.4) gives 1.059.
> I haven't been able to find what the meaning of fractional Hermite
> polynomials in Abramovitz. I have also tried inputing the Hermite
> differential equation, both with integer order and with fractional
> orders but Mathematica doesn't recognize it as a standard differential
> eqn as it does the Bessel equation. Anyone know more about this?
> (Mathematica does the same for Legendre polynomials)
> 
> vijay

you can look at Lebedev "Special function and their applications" Dover section 10.2 page 283 and following
Cheers, Enrico



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