15.9 Parabolic Cylinder Functions

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.

Function: parabolic_cylinder_d (v, z) ¶

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.

Categories: Special functions ·