POCH

The Pochhammer symbol, also called the rising factorial, is a core special function in series expansions, hypergeometric functions, and combinatorial identities.

It is defined by a gamma-function ratio:

(z)_m = \frac{\Gamma(z+m)}{\Gamma(z)}

and for positive integer m it equals the product z(z+1)\cdots(z+m-1). This wrapper computes (z)_m for real inputs.

Excel Usage

=POCH(z, m)

• z (float, required): Base argument of the rising factorial.
• m (float, required): Rising amount parameter.

Returns (float): Rising factorial (Pochhammer symbol) value.

Example 1: Pochhammer with zero rise equals one

Inputs:

z	m
4	0

Excel formula:

=POCH(4, 0)

Expected output:

1

Example 2: Pochhammer from one matches factorial-like value

Inputs:

z	m
1	5

Excel formula:

=POCH(1, 5)

Expected output:

120

Example 3: Pochhammer with fractional parameters

Inputs:

z	m
3.7	2.1

Excel formula:

=POCH(3.7, 2.1)

Expected output:

20.5296

Example 4: Pochhammer with integer-like parameters

Inputs:

z	m
2	3

Excel formula:

=POCH(2, 3)

Expected output:

24

Python Code

from scipy.special import poch as scipy_poch

def poch(z, m):
    """
    Evaluate the rising factorial using the Pochhammer symbol.

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

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

    Args:
        z (float): Base argument of the rising factorial.
        m (float): Rising amount parameter.

    Returns:
        float: Rising factorial (Pochhammer symbol) value.
    """
    try:
        return float(scipy_poch(z, m))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

z *

Base argument of the rising factorial.

m *

Rising amount parameter.