ERFCX

The scaled complementary error function improves numerical stability for large positive arguments by multiplying \mathrm{erfc}(x) by e^{x^2}.

\mathrm{erfcx}(x)=e^{x^2}\,\mathrm{erfc}(x)

This wrapper evaluates \mathrm{erfcx}(x) for a scalar real argument using SciPy.

Excel Usage

=ERFCX(x)

• x (float, required): Real argument for the scaled complementary error function (dimensionless).

Returns (float): Scaled complementary error function value at the input.

Example 1: Scaled complementary error function at zero

Inputs:

x
0

Excel formula:

=ERFCX(0)

Expected output:

1

Example 2: Scaled complementary error function at one

Inputs:

x
1

Excel formula:

=ERFCX(1)

Expected output:

0.427584

Example 3: Scaled complementary error function at two

Inputs:

x
2

Excel formula:

=ERFCX(2)

Expected output:

0.255396

Example 4: Scaled complementary error function at negative one

Inputs:

x
-1

Excel formula:

=ERFCX(-1)

Expected output:

5.00898

Python Code

from scipy.special import erfcx as scipy_erfcx

def erfcx(x):
    """
    Evaluate the exponentially scaled complementary error function.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.erfcx.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        x (float): Real argument for the scaled complementary error function (dimensionless).

    Returns:
        float: Scaled complementary error function value at the input.
    """
    try:
        x = float(x)
        return float(scipy_erfcx(x))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

Real argument for the scaled complementary error function (dimensionless).