Add python implementation

Author: antonwolfy

doc/reference/special.rst

@@ -15,6 +15,5 @@ Error function and Fresnel integrals
    erf
    erfc
    erfcx
-   erfi
    erfinv
    erfcinv

dpnp/special/__init__.py

@@ -42,9 +42,11 @@
 from ._erf import (
     erf,
     erfc,
+    erfcx,
 )
 
 __all__ = [
     "erf",
     "erfc",
+    "erfcx",
 ]

dpnp/special/_erf.py

@@ -42,7 +42,7 @@
 import dpnp.backend.extensions.ufunc._ufunc_impl as ufi
 from dpnp.dpnp_algo.dpnp_elementwise_common import DPNPUnaryFunc
 
-__all__ = ["erf", "erfc"]
+__all__ = ["erf", "erfc", "erfcx"]
 
 
 # pylint: disable=too-few-public-methods
@@ -96,7 +96,6 @@ def __call__(self, x, out=None):  # pylint: disable=signature-differs
 :obj:`dpnp.special.erfinv` : Inverse of the error function.
 :obj:`dpnp.special.erfcinv` : Inverse of the complementary error function.
 :obj:`dpnp.special.erfcx` : Scaled complementary error function.
-:obj:`dpnp.special.erfi` : Imaginary error function.
 
 Notes
 -----
@@ -152,7 +151,6 @@ def __call__(self, x, out=None):  # pylint: disable=signature-differs
 :obj:`dpnp.special.erfinv` : Inverse of the error function.
 :obj:`dpnp.special.erfcinv` : Inverse of the complementary error function.
 :obj:`dpnp.special.erfcx` : Scaled complementary error function.
-:obj:`dpnp.special.erfi` : Imaginary error function.
 
 Examples
 --------
@@ -171,3 +169,48 @@ def __call__(self, x, out=None):  # pylint: disable=signature-differs
     mkl_fn_to_call="_mkl_erf_to_call",
     mkl_impl_fn="_erfc",
 )
+
+_ERFCX_DOCSTRING = r"""
+Calculates the scaled complementary error function of a given input array.
+
+It is defined as :math:`\exp(x^2) * \operatorname{erfc}(x)`.
+
+For full documentation refer to :obj:`scipy.special.erfcx`.
+
+Parameters
+----------
+x : {dpnp.ndarray, usm_ndarray}
+    Input array, expected to have a real-valued floating-point data type.
+out : {dpnp.ndarray, usm_ndarray}, optional
+    Optional output array for the function values.
+
+Returns
+-------
+out : dpnp.ndarray
+    The values of the scaled complementary error function at the given points
+    `x`.
+
+See Also
+--------
+:obj:`dpnp.special.erf` : Gauss error function.
+:obj:`dpnp.special.erfc` : Complementary error function.
+:obj:`dpnp.special.erfinv` : Inverse of the error function.
+:obj:`dpnp.special.erfcinv` : Inverse of the complementary error function.
+
+Examples
+--------
+>>> import dpnp as np
+>>> x = np.linspace(-3, 3, num=4)
+>>> np.special.erfcx(x)
+array([1.62059889e+04, 5.00898008e+00, 4.27583576e-01, 1.79001151e-01])
+
+"""
+
+erfcx = DPNPErf(
+    "erfcx",
+    ufi._erf_result_type,
+    ufi._erfcx,
+    _ERFCX_DOCSTRING,
+    mkl_fn_to_call="_mkl_erf_to_call",
+    mkl_impl_fn="_erfcx",
+)