RGAMMA

The reciprocal gamma function is defined as the inverse of the gamma function and is often used to avoid overflow in formulas that place gamma terms in denominators.

It is given by:

\operatorname{rgamma}(x)=\frac{1}{\Gamma(x)}

Unlike \Gamma(x), this reciprocal form is entire and has zeros at nonpositive integers.

Excel Usage

=RGAMMA(x)

• x (float, required): Real argument for the reciprocal gamma function.

Returns (float): Reciprocal gamma function value at the input.

Example 1: Reciprocal gamma at one

Inputs:

x
1

Excel formula:

=RGAMMA(1)

Expected output:

1

Example 2: Reciprocal gamma at four

Inputs:

x
4

Excel formula:

=RGAMMA(4)

Expected output:

0.166667

Example 3: Reciprocal gamma at one-half

Inputs:

x
0.5

Excel formula:

=RGAMMA(0.5)

Expected output:

0.56419

Example 4: Reciprocal gamma at a nonpositive integer

Inputs:

x
0

Excel formula:

=RGAMMA(0)

Expected output:

0

Python Code

from scipy.special import rgamma as scipy_rgamma

def rgamma(x):
    """
    Compute the reciprocal of the gamma function.

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

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

    Args:
        x (float): Real argument for the reciprocal gamma function.

    Returns:
        float: Reciprocal gamma function value at the input.
    """
    try:
        return float(scipy_rgamma(x))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

Real argument for the reciprocal gamma function.