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Hermite Differential Equation

• To: mathgroup at yoda.physics.unc.edu
• Subject: Hermite Differential Equation
• From: ALBERGOTTI at alm.admin.usfca.edu
• Date: Wed, 15 Dec 1993 14:20:27 -0800 (PST)

	The Mma command DSolve doesn't seem to recognize that the solution
to the differential equation,

	g''[t] - 2*t*g'[t] + w*g[t] == 0   ,

involves Hermite polynomials.  Perhaps I need to inform Mma that w is a non-
negative integer.  If I let w = 2, for example, then DSolve returns

	g[t] -> t C[1] - E^(t^2) C[2] + Sqrt[Pi] t C[2] Erfi[t]   ,

which surprised me because I didn't expect the error function in this
context.  This would be the expected Hermite polynomial if C[1] = 2
and C[2] = 0.  Can anyone suggest a better way to proceed?