ELLIPRF

Carlson’s symmetric integral R_F is a three-argument elliptic integral used to express Legendre forms in a numerically stable symmetric representation.

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

This wrapper evaluates R_F for scalar real inputs in its valid domain.

Excel Usage

=ELLIPRF(x, y, z)

x (float, required): First nonnegative real parameter.
y (float, required): Second nonnegative real parameter.
z (float, required): Third nonnegative real parameter.

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

Example 1: Carlson RF with positive parameters

Inputs:

x	y	z
1	2	3

Excel formula:

=ELLIPRF(1, 2, 3)

Expected output:

0.726946

Example 2: Carlson RF with one zero parameter

Inputs:

x	y	z
0	1	2

Excel formula:

=ELLIPRF(0, 1, 2)

Expected output:

1.31103

Example 3: Carlson RF when all parameters are equal

Inputs:

x	y	z
2	2	2

Excel formula:

=ELLIPRF(2, 2, 2)

Expected output:

0.707107

Example 4: Carlson RF with fractional parameters

Inputs:

x	y	z
0.5	1.5	2.5

Excel formula:

=ELLIPRF(0.5, 1.5, 2.5)

Expected output:

0.861996

Python Code

from scipy.special import elliprf as scipy_elliprf

def elliprf(x, y, z):
    """
    Compute Carlson's completely symmetric elliptic integral RF.

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

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

    Args:
        x (float): First nonnegative real parameter.
        y (float): Second nonnegative real parameter.
        z (float): Third nonnegative real parameter.

    Returns:
        float: Value of Carlson symmetric elliptic integral RF.
    """
    try:
        return float(scipy_elliprf(x, y, z))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

First nonnegative real parameter.

y *

Second nonnegative real parameter.

z *

Third nonnegative real parameter.