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?