GAMMA

The gamma function extends the factorial to non-integer real values through an integral definition and analytic continuation. For positive integers, it satisfies \Gamma(n+1)=n!, making it a fundamental building block in probability, statistics, and special-function identities.

For real x>0, it is defined by:

\Gamma(x)=\int_0^{\infty} t^{x-1}e^{-t}\,dt

This wrapper computes \Gamma(x) for a scalar real argument using SciPy’s special functions implementation.

Excel Usage

=GAMMA(x)

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

Returns (float): Gamma function value at the input.

Example 1: Gamma at one-half

Inputs:

x
0.5

Excel formula:

=GAMMA(0.5)

Expected output:

1.77245

Example 2: Gamma at six equals factorial of five

Inputs:

x
6

Excel formula:

=GAMMA(6)

Expected output:

120

Example 3: Gamma at positive fractional input

Inputs:

x
2.5

Excel formula:

=GAMMA(2.5)

Expected output:

1.32934

Example 4: Gamma at negative non-integer input

Inputs:

x
-0.5

Excel formula:

=GAMMA(-0.5)

Expected output:

-3.54491

Python Code

from scipy.special import gamma as scipy_gamma

def gamma(x):
    """
    Evaluate the gamma function for a real input.

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

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

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

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

Online Calculator

x *

Real argument for the gamma function.