DIGAMMA Function (Gnumeric)

• Introduced: Gnumeric 1.12.45 release notes explicitly record this function being added.
• Supported in: Gnumeric 1.12.62, with no retirement established.
• Scope: Desktop Gnumeric with the Mathematics plugin; English comma-separated formulas are shown.
• Checked: October 14, 2026. Reference and boundary tables plus the explicit advanced-check formula were recalculated through 1.12.57 ssconvert. Current 1.12.62 source was inspected; that later release was not executed.

DIGAMMA evaluates ψ(x), the logarithmic derivative of the gamma function. For positive x, ψ(x)=d lnΓ(x)/dx. It is neither Γ(x) nor lnΓ(x). The result can be negative, zero or positive depending on x. Versioned function help.

=DIGAMMA(x)

Exactly one numeric x is required. Positive values provide the ordinary real domain. Negative nonintegers are also evaluated through a reflection formula, while zero and negative integers are poles and produce #NUM!. Values very close to a pole require special care. Function implementation.

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

The reference values at 1,2 and 3 are approximately −0.577215664902, 0.422784335098, and 0.922784335098. Put those inputs in A2:A4 and fill =DIGAMMA(A2) down to inspect the same mathematical sequence.

For a positive integer n, ψ(n)=H(n−1)−γ, where H is a harmonic number and γ is the Euler–Mascheroni constant. At n=3,1+1/2−γ gives the reference 0.922784335098. This identity is a useful independent check without calculating a numerical derivative.

The recurrence ψ(x+1)=ψ(x)+1/x holds away from its poles. The executed residual =DIGAMMA(2.5)-DIGAMMA(1.5)-1/1.5 returned 0. In floating-point calculations, nearby cases can leave a small nonzero residual and should be assessed with an appropriate tolerance.

The negative noninteger examples distinguish poles from a blanket nonpositive-input prohibition. DIGAMMA(−0.5) is approximately 0.036489973979, and DIGAMMA(−1.5) is approximately 0.703156640645. They are finite; DIGAMMA(−1) is not.

The positive root is near 1.461632144968, so DIGAMMA(1.46) is close to zero but not exactly zero. A small displayed value near the root can have a large relative rounding error while its absolute error remains small. Avoid interpreting a rounded zero as an exact root.

The source’s negative-input reflection formula has its own numerical sensitivities near zeros and poles. The native tests establish only the listed arguments, not universal precision. An empty F5 becomes the pole at zero in this fixture and produces #NUM!, while TRUE becomes 1.

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

• Worksheet entry
• Numeric or argument-handling source

The retained workbook results include a deliberately stale SUM cache and an uncached SUM formula, both recalculated correctly. Native evidence covers the named 1.12.57 build and listed cases; cell-reference layouts and other explanatory compositions are instructions or independent mathematical checks unless explicitly identified as executed. Other locales, direct GUI entry and later-release output were not tested.