### 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 ·