POCHHAMMER Function (Gnumeric)

• Introduced: Gnumeric 1.12.2 release notes explicitly record this function being added. Negative-value support was extended in 1.12.10.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with the Mathematics plugin. English comma-separated formulas are shown.
• Checked: October 14, 2026. Tables and the named advanced check were recalculated through 1.12.57 ssconvert. Current 1.12.62 source was inspected; the later release was not executed.

POCHHAMMER(x,n) represents Γ(x+n)/Γ(x). For a nonnegative integer n and nonsingular ordinary inputs, it is the rising factorial x(x+1)…(x+n−1). The function also accepts fractional and negative n, so it is broader than a repeated-product formula. Its negative-integer boundary rules need separate attention. Versioned function help.

=POCHHAMMER(x,n)

Function implementation.

Ordinary results are rounded to twelve decimal places; tiny values use scientific notation. The eight reference rows were independently checked.

For three consecutive factors starting at 2, =POCHHAMMER(2,3) returns 24, matching 2 × 3 × 4. The executed difference =POCHHAMMER(2,3)-2*3*4 returned zero. For five factors starting at 1, the result is 120, the same as 5 factorial.

Fractional increments have no literal “half a factor” interpretation. =POCHHAMMER(6,0.5) returned approximately 2.399043981792, evaluated as Γ(6.5)/Γ(6). Use the gamma-ratio definition when n is not an integer, while checking that the required values exist.

For valid arguments, the identity (x)ₙ₊₁ = (x+n)(x)ₙ follows immediately from Γ(z+1) = zΓ(z). At x = 2, n = 3, the next rising product is 5 × 24 = 120. For negative increments, =POCHHAMMER(2,-1) gives Γ(1)/Γ(2) = 1.

Do not implement the function by naively dividing two separately calculated gamma values when either could overflow or be singular. The current helper has scaled calculations and explicit branches. It can return a defined finite value such as POCHHAMMER(−3,2) = 6 even though separately evaluating the two gamma factors at their poles is unsuitable.

The native implementation is not an unrestricted polynomial extension at negative integers. =POCHHAMMER(-3,4) returned #NUM!, even though the four-factor polynomial product includes zero. Conversely, POCHHAMMER(0,2) returned zero and POCHHAMMER(0,0) returned one. The source contains explicit special cases behind these distinctions. Keep the tested error cases visible rather than replacing all singular-looking inputs with zero.

F5 is an actually empty cell. Listed errors are native error results, not mathematical zeroes.

• Worksheet implementation
• Numeric helper or conversion source

The retained workbook contained a deliberately stale SUM cache and an uncached SUM formula, both recalculated correctly. Native evidence covers the listed 1.12.57 cases; worksheet layouts and algebraic interpretations are independently specified explanations. Other locales, direct GUI entry and later-release output were not tested.

GAMMA, FACT.