

@defun
def pcfu(ctx, a, z, **kwargs):
    "\n    Gives the parabolic cylinder function `U(a,z)`, which may be\n    defined for `\\Re(z) > 0` in terms of the confluent\n    U-function (see :func:`~mpmath.hyperu`) by\n\n    .. math ::\n\n        U(a,z) = 2^{-\\frac{1}{4}-\\frac{a}{2}} e^{-\\frac{1}{4} z^2}\n            U\\left(\\frac{a}{2}+\\frac{1}{4},\n            \\frac{1}{2}, \\frac{1}{2}z^2\\right)\n\n    or, for arbitrary `z`,\n\n    .. math ::\n\n        e^{-\\frac{1}{4}z^2} U(a,z) =\n            U(a,0) \\,_1F_1\\left(-\\tfrac{a}{2}+\\tfrac{1}{4};\n            \\tfrac{1}{2}; -\\tfrac{1}{2}z^2\\right) +\n            U'(a,0) z \\,_1F_1\\left(-\\tfrac{a}{2}+\\tfrac{3}{4};\n            \\tfrac{3}{2}; -\\tfrac{1}{2}z^2\\right).\n\n    **Examples**\n\n    Connection to other functions::\n\n        >>> from mpmath import *\n        >>> mp.dps = 25; mp.pretty = True\n        >>> z = mpf(3)\n        >>> pcfu(0.5,z)\n        0.03210358129311151450551963\n        >>> sqrt(pi/2)*exp(z**2/4)*erfc(z/sqrt(2))\n        0.03210358129311151450551963\n        >>> pcfu(0.5,-z)\n        23.75012332835297233711255\n        >>> sqrt(pi/2)*exp(z**2/4)*erfc(-z/sqrt(2))\n        23.75012332835297233711255\n        >>> pcfu(0.5,-z)\n        23.75012332835297233711255\n        >>> sqrt(pi/2)*exp(z**2/4)*erfc(-z/sqrt(2))\n        23.75012332835297233711255\n\n    "
    (n, _) = ctx._convert_param(a)
    return ctx.pcfd(((- kwargs) - ctx.mpq_1_2), z)

dataset/ETHPy150Open fredrik-johansson/mpmath/mpmath/functions/orthogonal.py pcfu/VarMisuse@43/684 `n`->`kwargs`