ERFI

The imaginary error function is defined through the standard error function by analytic continuation and is commonly used in wave and plasma integrals.

\mathrm{erfi}(x)=-i\,\mathrm{erf}(ix)

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

Excel Usage

=ERFI(x)

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

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

Example 1: Imaginary error function at zero

Inputs:

x
0

Excel formula:

=ERFI(0)

Expected output:

0

Example 2: Imaginary error function at one half

Inputs:

x
0.5

Excel formula:

=ERFI(0.5)

Expected output:

0.614952

Example 3: Imaginary error function at one

Inputs:

x
1

Excel formula:

=ERFI(1)

Expected output:

1.65043

Example 4: Imaginary error function at negative one

Inputs:

x
-1

Excel formula:

=ERFI(-1)

Expected output:

-1.65043

Python Code

from scipy.special import erfi as scipy_erfi

def erfi(x):
    """
    Evaluate the imaginary error function for a real input.

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

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

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

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

Online Calculator

x *

Real argument for the imaginary error function (dimensionless).