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Extension to parabolic cylinder functions?
Posted:
Feb 9, 2012 7:52 AM


Hi,
The socalled parabolic cylinder functions are known to represent the solutions of the ordinary differential equation
d^2 u(x)/ dx^2 (a*x^2 +b*x + c) * u(x) = 0
When a = 0 the equation reduces to the Airy equation, with Airy functions as solutions.
I am trying to solve an equation with a fourth order polynomial in the place of the second order one:
d^2 u(x)/ dx^2 (a*x^4 + b*x^3 + c*x^2 + d*x + e) * u(x) = 0
My question is: are there any extensions of the parabolic cylinder functions to the above equation? Do there exist any special functions that represent solutions of the equation?
I would appreciate any pointers.
Leslaw



