Syntax
GAMMALN(x)
| Parameter | Description |
|---|---|
| x | Parameter of the GAMMALN function. |
Examples
Log-gamma of 5 (related to 4!)
Formula
=GAMMALN(5)
Returns ~3.178. Since gamma(5) = 4! = 24, GAMMALN(5) = LN(24) = 3.178.
Computing binomial coefficient
Formula
=EXP(GAMMALN(21)-GAMMALN(6)-GAMMALN(16))
Returns 20349. This calculates C(20,5) = 20!/(5!*15!) using log-gamma to avoid factorial overflow.
Half-integer argument
Formula
=GAMMALN(0.5)
Returns ~0.5724. Gamma(0.5) = sqrt(pi) = 1.7725, so GAMMALN(0.5) = LN(1.7725) = 0.5724.
Common Errors
#NUM!
x must be positive. GAMMALN is undefined for zero and negative values.
#VALUE!
Occurs when the argument is non-numeric text.
Tips
Avoid overflow
Use GAMMALN instead of computing factorials directly. Factorials grow extremely fast — 170! overflows standard floating point, but GAMMALN(171) works fine.
Recover the gamma value
To get the actual gamma function value, use =EXP(GAMMALN(x)). But only do this when the result is small enough not to overflow.
Combinatorial calculations
For combinations C(n,k), use =EXP(GAMMALN(n+1) - GAMMALN(k+1) - GAMMALN(n-k+1)). This works for much larger values than direct factorial computation.
Try GAMMALN in Viztab
Import your data and use GAMMALN with 370+ other formulas. No signup required.
Open Viztab