LAMBERTW Function (Gnumeric)

• Introduced: Gnumeric 1.12.44 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.

LAMBERTW finds a real w satisfying w × exp(w) = x. For negative x between −1/e and zero there are two real solutions, so choosing the branch is part of the problem rather than a cosmetic option. Versioned function help.

=LAMBERTW(x[,branch])

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.

To solve w × exp(w) = 3, use =LAMBERTW(3), approximately 1.049908894964. Substituting this solution into w × exp(w) reconstructs 3. The executed residual =LAMBERTW(3)*EXP(LAMBERTW(3))-3 was approximately −4.440892098501E−16, close to zero at floating-point precision.

For x = −0.25, the principal solution is approximately −0.357402956181; branch −1 gives approximately −2.153292364110. Both solve the same equation. Choose the one consistent with the range required by your model: the principal branch has w ≥ −1, whereas the lower branch has w ≤ −1.

An equation of the form y × exp(c × y) = d can be transformed by multiplying by c: set w = c × y, then w × exp(w) = c × d. For nonzero c, an independent algebraic solution is y = LAMBERTW(c × d, branch)/c. The required real-domain and branch restrictions apply to c × d.

The table includes =LAMBERTW(2*EXP(2)), which returned 2. At x = −1/e the two branches meet at −1. Near this meeting point the inverse is sensitive to small changes in x; keep sufficient input precision rather than judging correctness solely from displayed decimals.

Zero is allowed on the principal branch but not as a finite value on branch −1. The latter tends toward negative infinity as x approaches zero from below, and the tested exact-zero call returned #NUM!. Fractional branch labels are rejected rather than truncated. The source explicitly accommodates the rounded −1/e endpoint, matching the two tested endpoint calls.

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.

EXP, LOG.