code: def pcfd(ctx, n, z, **kwargs):
      r"""
      Gives the parabolic cylinder function in Whittaker's notation
      `D_n(z) = U(-n-1/2, z)` (see :func:`~mpmath.pcfu`).
      It solves the differential equation
  
      .. math ::
  
          y'' + \left(n + \frac{1}{2} - \frac{1}{4} z^2\right) y = 0.
  
      and can be represented in terms of Hermite polynomials
      (see :func:`~mpmath.hermite`) as
  
      .. math ::
  
          D_n(z) = 2^{-n/2} e^{-z^2/4} H_n\left(\frac{z}{\sqrt{2}}\right).
  
      **Plots**
  
      .. literalinclude :: /plots/pcfd.py
      .. image :: /plots/pcfd.png
  
      **Examples**
  
          >>> from mpmath import *
          >>> mp.dps = 25; mp.pretty = True
          >>> pcfd(0,0); pcfd(1,0); pcfd(2,0); pcfd(3,0)
          1.0
          0.0
          -1.0
          0.0
          >>> pcfd(4,0); pcfd(-3,0)
          3.0
          0.6266570686577501256039413
          >>> pcfd('1/2', 2+3j)
          (-5.363331161232920734849056 - 3.858877821790010714163487j)
          >>> pcfd(2, -10)
          1.374906442631438038871515e-9
  
      Verifying the differential equation::
  
          >>> n = mpf(2.5)
          >>> y = lambda z: pcfd(n,z)
          >>> z = 1.75
          >>> chop(diff(y,z,2) + (n+0.5-0.25*z**2)*y(z))
          0.0
  
      Rational Taylor series expansion when `n` is an integer::
  
          >>> taylor(lambda z: pcfd(5,z), 0, 7)
          [0.0, 15.0, 0.0, -13.75, 0.0, 3.96875, 0.0, -0.6015625]
  
      """
      return ctx.hypercomb(
          lambda: _hermite_param(ctx, n, z, 1), [], **kwargs
      )
  
file_path: catboost/contrib/python/mpmath/py3/mpmath/functions/orthogonal.py
imports: from .functions import defun, defun_wrapped
label_desc: Use image node_id 3 for calling a global function with example usage: pcfd(ctx, n, z) and returns: ctx