IGAMMA Function (Gnumeric)

• Introduced: Gnumeric 1.12.10 release notes explicitly record this function being added.
• 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.

For positive a and nonnegative x, the lower incomplete gamma integral runs from 0 to x, while the upper integral runs from x to infinity. IGAMMA defaults to the lower result divided by Γ(a). This regularized value is often written P(a,x); its upper counterpart is Q(a,x). The final argument selects one real-valued component when the result is complex. Versioned function help.

=IGAMMA(a,x[,lower[,regularize[,real]]])

Brackets mark optional arguments; do not type the brackets. Function implementation.

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

For a gamma-distributed quantity with shape 2 and scale 1, =IGAMMA(2,1) gives approximately 0.264241117657 below x = 1. =IGAMMA(2,1,FALSE()) gives approximately 0.735758882343 above it. For a positive scale θ other than 1, use x/θ as the second argument. This probability interpretation assumes a positive shape and scale.

At shape 3, Γ(3) = 2. The table’s unregularized lower result is therefore twice the regularized result. Leaving the fourth argument at its default changes the mathematical quantity, not just its display format.

For integer shape 2, independent integration gives P(2,x) = 1 − exp(−x)(1 + x). At x = 1 this is 1 − 2/e. The executed complement check =IGAMMA(2,1)+IGAMMA(2,1,FALSE()) returned 1. Compute an upper tail directly rather than subtracting a lower result extremely close to 1, which can lose small-tail precision.

Negative x may produce a complex value. The tested a = 2.5, x = −1.8 case returned real component 0 and imaginary component approximately 5.056872568915. Use separate calls with the fifth argument TRUE and FALSE if both components matter; a zero real component alone does not mean the full value is zero.

At nonpositive integer a, the ordinary defining integral or gamma quotient can be singular. The source has an explicit regularized extension: the tested lower results at a = 0 and a = −1 were both 1. These values must not be interpreted as probabilities from a valid positive-shape gamma distribution. Omitted optional arguments default to TRUE; an omitted required argument gives #N/A.

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, GAMMALN.