ELLIPRC

Carlson’s degenerate symmetric integral R_C is a two-argument special case of R_F and can be written as:

R_C(x,y)=\frac{1}{2}\int_0^{\infty}(t+x)^{-1/2}(t+y)^{-1}\,dt

It also satisfies R_C(x,y)=R_F(x,y,y). This wrapper evaluates R_C for scalar real inputs with nonzero y.

Excel Usage

=ELLIPRC(x, y)

x (float, required): First real parameter.
y (float, required): Second real parameter; must be nonzero.

Returns (float): Value of Carlson degenerate symmetric elliptic integral RC.

Example 1: Carlson RC with positive parameters

Inputs:

x	y
1	2

Excel formula:

=ELLIPRC(1, 2)

Expected output:

0.785398

Example 2: Carlson RC when both parameters are equal

Inputs:

x	y
2	2

Excel formula:

=ELLIPRC(2, 2)

Expected output:

0.707107

Example 3: Carlson RC with zero first parameter

Inputs:

x	y
0	2

Excel formula:

=ELLIPRC(0, 2)

Expected output:

1.11072

Example 4: Carlson RC with fractional parameters

Inputs:

x	y
0.5	1.5

Excel formula:

=ELLIPRC(0.5, 1.5)

Expected output:

0.955317

Python Code

from scipy.special import elliprc as scipy_elliprc

def elliprc(x, y):
    """
    Compute Carlson's degenerate symmetric elliptic integral RC.

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

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

    Args:
        x (float): First real parameter.
        y (float): Second real parameter; must be nonzero.

    Returns:
        float: Value of Carlson degenerate symmetric elliptic integral RC.
    """
    try:
        if y == 0:
            return "Error: y must be nonzero"
        return float(scipy_elliprc(x, y))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

First real parameter.

y *

Second real parameter; must be nonzero.