BETA Function (Gnumeric)

• Introduced: Documented by 1.12.62; original introduction not established.
• Availability: Supported in Gnumeric 1.12.62, based on the function-specific registration.
• Scope: Desktop; the fn-math function module must be included and enabled.
• Checked: October 14, 2026. Official source and independent mathematical examples checked; Gnumeric 1.12.62 was not run.

BETA evaluates Euler’s beta special function B(x,y). It is not a beta-distribution cumulative probability. With positive parameters it often acts as the normalizing constant for a beta density. Official function reference.

For x,y>0, B(x,y)=Γ(x)Γ(y)/Γ(x+y), equivalently the integral of t^(x−1)(1−t)^(y−1) from 0 to 1. The function is symmetric: B(x,y)=B(y,x). Gnumeric extends it to additional real arguments outside the integral’s positive-parameter domain.

=BETA(x,y)

Every argument shown is required. Use numeric inputs or cell references. The examples follow English Gnumeric’s comma-separated notation and decimal points; localized separators can differ. Release-pinned argument help and evaluator.

Enter each formula in an unused worksheet cell. These are independently calculated mathematical reference values rounded to twelve decimal places. Keep full stored precision in later formulas rather than retyping a rounded display.

Normalize a beta density

For positive parameters a=2 and b=3, =BETA(2,3) gives 0.083333333333, or 1/12. At t=0.4, the density formula =0.4^(2-1)*(1-0.4)^(3-1)/BETA(2,3) has expected value 1.728. A density exceeding 1 is valid; probability is its integral over an interval.

Check a recurrence without large Gamma values

B(a+1,b)=a/(a+b)×B(a,b). For a=2 and b=3, compare =BETA(3,3) with =2/(2+3)*BETA(2,3). Both give 0.033333333333. The equality is a useful check when a model involves adjacent parameter values.

Zero or negative integer individual arguments are rejected by the release helper and become #NUM!. One documentation exception matters: the help also says a nonpositive integer x+y gives #NUM!, but the pinned helper returns zero for that sum when neither individual argument is a pole. Thus =BETA(-0.5,0.5) has source-backed expected value 0. Do not generalize the positive-parameter integral to this continuation. Pinned evaluator. Beta-domain and continuation implementation. Nonfinite numeric result handling.

For negative noninteger arguments, BETA can be negative: BETA(−0.5,1.5)=−π. Such arguments are not valid beta-distribution shape parameters. When only the logarithmic magnitude is required, BETALN avoids taking a logarithm of a negative result and can reduce overflow risk. It intentionally discards the sign.

BETALN; GAMMA; BETA.DIST.

• BETA manual entry
• Gnumeric 1.12.62 argument contract and calculation
• Beta-domain and continuation implementation
• Nonfinite numeric result handling