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

$$y^{″}(z)+(\nu +\frac{1}{2}-\frac{1}{4}{z}^2)y(z)=0$$

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 ·