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Hermite Polynomials of fractional order

• To: mathgroup at smc.vnet.net
• Subject: [mg4601] Hermite Polynomials of fractional order
• From: pvfafat at gsbphd5.uchicago.edu (Vijay Fafat)
• Date: Wed, 21 Aug 1996 03:25:20 -0400
• Organization: GSB, University of Chicago
• Sender: owner-wri-mathgroup at wolfram.com

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

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