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The Parabolic Cylinder Functions are defined in Abramowitz and Stegun, Handbook of Mathematical Functions, A&S Chapter 19.
Maxima has very limited knowledge of these functions. They
can be returned from function specint.
The parabolic cylinder function parabolic_cylinder_d(v,z). (A&S eqn 19.3.1).
The solution of the Weber differential equation $$ y''(z) + \left(\nu + {1\over 2} - {1\over 4} z^2\right) y(z) = 0 $$
has two independent solutions, one of which is \(D_{\nu}(z)\), the parabolic cylinder d function.
Function specint can return expressions containing
parabolic_cylinder_d(v,z) if the option variable
prefer_d is true.
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