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### 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 ·

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