DIGAMMA

The digamma function is the first logarithmic derivative of the gamma function and appears in optimization, Bayesian updates, and asymptotic expansions involving gamma terms.

It is defined as:

\psi(x)=\frac{d}{dx}\ln\Gamma(x)

This wrapper evaluates the real-valued digamma function using SciPy’s implementation.

Excel Usage

=DIGAMMA(x)

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

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

Example 1: Digamma at one

Inputs:

x
1

Excel formula:

=DIGAMMA(1)

Expected output:

-0.577216

Example 2: Digamma at two

Inputs:

x
2

Excel formula:

=DIGAMMA(2)

Expected output:

0.422784

Example 3: Digamma at positive fraction

Inputs:

x
0.5

Excel formula:

=DIGAMMA(0.5)

Expected output:

-1.96351

Example 4: Digamma at larger positive input

Inputs:

x
10

Excel formula:

=DIGAMMA(10)

Expected output:

2.25175

Python Code

from scipy.special import digamma as scipy_digamma

def digamma(x):
    """
    Compute the digamma function for a real input.

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

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

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

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

Online Calculator

x *

Real argument for the digamma function.