PlanMaker GAMMA: Positive Inputs, Factorials and Recurrences

The PlanMaker 2026 reference, 2024 reference and 2021 reference document this function. Original introduction and last-working-version endpoints remain unverified; a manual family is not a test of every build or edition.

References were retrieved on October 15, 2026. No native PlanMaker execution was performed. Examples below are independently calculated expectations, not application screenshots or native results. FreeOffice/mobile edition coverage and file transfers are not certified. English formulas use commas; verify separators and names in your installation.

=GAMMA(Number)

Number is required and must be greater than zero in the PlanMaker reference. Do not extend this documented domain to negative nonintegers just because the mathematical gamma function can be continued there, or because another spreadsheet allows them. The checked reference does not identify an exact native error for zero or negative inputs.

The manual’s Excel 2013 compatibility note describes Excel, not PlanMaker’s introduction date. It does not prove identical coercion, overflow limits or negative-argument behavior.

For positive real x, the NIST definition is the integral of exp(−t)t^(x−1) from zero to infinity. This is the gamma function, not a gamma probability distribution or its cumulative probability. GAMMA takes one shape-like numeric argument; it does not take a scale parameter or cumulative flag.

Create GammaControls with Input in A1, Gamma in B1 and Next_argument in C1. Enter A2:A7 below, fill B2 =GAMMA(A2) and C2 =GAMMA(A2+1) down.

In a copy change A4 from 1.5 to 2.5. Expected B4 becomes 1.3293403882 and C4 becomes 3.3233509704. Keep the original inputs for comparison. Printed decimals are rounded to ten places; native final-digit accuracy is untested.

For a positive integer n, Γ(n)=(n−1)!. Thus =GAMMA(6) has expected result 120, while =GAMMA(5) is 24. To represent 5!, the argument is 6. Passing 5 is an off-by-one error even though it returns a perfectly valid number.

Create FactorialControls with integers 1,2,3,4,5 in F2:F6. Fill G2 =GAMMA(F2+1) down. Expected results are 1,2,6,24,120. This small-integer dataset checks the meaning without relying on very large factorial values or an undocumented overflow boundary.

NIST’s recurrence gives Γ(x+1)=xΓ(x). On GammaControls fill D2 =A2*B2 down. D should agree mathematically with C for every positive input in the table. In E2 use =C2-D2 and fill down; the exact mathematical residual is zero.

A tiny floating-point residual in an installed application is not automatically a wrong formula. Compare at a tolerance appropriate to the magnitudes, and do not compare rounded screen strings. This is a consistency check, not a native accuracy certification.

For x=3.5, =GAMMA(5.5)/GAMMA(3.5) has expected result 15.75, because the recurrence reduces the ratio to 4.5×3.5. If the starting input changes to 4.5, the two-step ratio becomes 24.75. Put x in H2 and use =GAMMA(H2+2)/GAMMA(H2) so the relationship remains visible.

For large arguments, separate gamma evaluations can become too large even when a ratio is manageable. GAMMALN can represent logarithms of gamma values, but exponentiating a large log difference can still exceed a program’s numeric range. No native threshold is claimed here.

Keep inputs positive and numeric. The reference does not settle empty cells, text, Boolean values, arrays, extreme inputs or exact error codes outside its domain. Do not describe those as tested behavior. A negative output from a positive real input would conflict with the mathematical definition, but diagnosing it still requires the exact entered formula and application build.

Check the one-unit factorial offset, then check whether the intended task is a gamma function or a probability distribution. Record the PlanMaker edition, build, language and workbook format before extending these finite controls to sensitive numerical work.