EULER_BETA

The Euler beta function is a symmetric two-parameter special function that appears in probability distributions, integral transforms, and normalization constants.

It can be defined by an integral on [0,1] and by gamma functions:

B(a,b)=\int_0^1 t^{a-1}(1-t)^{b-1}\,dt

B(a,b)=\frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}

This wrapper evaluates B(a,b) using SciPy.

Excel Usage

=EULER_BETA(a, b)

• a (float, required): First real shape parameter.
• b (float, required): Second real shape parameter.

Returns (float): Beta function value for the given parameters.

Example 1: Beta with integer parameters

Inputs:

a	b
2	3

Excel formula:

=EULER_BETA(2, 3)

Expected output:

0.0833333

Example 2: Beta with non-integer parameters

Inputs:

a	b
1.7	2.4

Excel formula:

=EULER_BETA(1.7, 2.4)

Expected output:

0.165675

Example 3: Beta with first parameter equal to one

Inputs:

a	b
1	4

Excel formula:

=EULER_BETA(1, 4)

Expected output:

0.25

Example 4: Beta with small positive shape parameters

Inputs:

a	b
0.5	0.5

Excel formula:

=EULER_BETA(0.5, 0.5)

Expected output:

3.14159

Python Code

from scipy.special import beta as scipy_beta

def euler_beta(a, b):
    """
    Evaluate the Euler beta function for two real parameters.

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

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

    Args:
        a (float): First real shape parameter.
        b (float): Second real shape parameter.

    Returns:
        float: Beta function value for the given parameters.
    """
    try:
        return float(scipy_beta(a, b))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

a *

First real shape parameter.

b *

Second real shape parameter.