BETALN 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.

BETALN returns the natural logarithm of the absolute value of Euler’s beta function: ln|B(x,y)|. The absolute-value detail matters for Gnumeric’s real extensions, where BETA can be negative. Official function reference.

For positive x,y, ln B(x,y)=ln Γ(x)+ln Γ(y)−ln Γ(x+y). Computing in log space can avoid forming an extremely large or small intermediate beta value. The result is a logarithmic normalization constant, not a probability.

=BETALN(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.

Build a log-density

For a=2, b=3 and t=0.4, compute:

=(2-1)*LN(0.4)+(3-1)*LN(1-0.4)-BETALN(2,3)

The expected result is 0.546964670382, the logarithm of density 1.728. Applying EXP recovers that density. This formula requires 0<t<1 and positive shape parameters; endpoint log terms need separate limiting treatment.

Compare two normalizations

=EXP(BETALN(3,3)-BETALN(2,3)) has expected value 0.4. It forms a ratio through a difference of logarithms, which is often more stable than dividing two underflowed values. Avoid exponentiating an enormous final logarithm unless you actually need the ordinary-scale result.

The release calls gnm_lbeta3 and discards its separately computed sign, confirming the absolute-value contract. Zero or negative integer individual arguments lead to a numeric error. When x+y is a nonpositive integer while neither argument is a pole, BETA’s helper yields zero; ln|0| is nonfinite and BETALN consequently maps to #NUM!. Pinned evaluator. Beta-domain and continuation implementation. Nonfinite numeric result handling.

For x=−0.5 and y=1.5, BETA equals −π but BETALN equals ln π, approximately 1.144729885849. Therefore =EXP(BETALN(-0.5,1.5)) reconstructs π, not −π. Keep sign information separately if a non-statistical model uses the real extension. Positive beta-distribution shape parameters avoid that ambiguity.

BETA; GAMMALN.

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