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Statistical function
GAMMALN
Returns the natural logarithm of the gamma function.
Rarely usedDifficulty 1500 · AdvancedUsage rank #398 of 520
When to use it
The natural logarithm of the gamma function. Lets you work with factorials far too large to store directly.
The shape of it
- Syntax
=GAMMALN(x)
Worked examples
Small value
=GAMMALN(5) → 3.17805383
LN(24).
One
=GAMMALN(1) → 0
GAMMA(1) is 1.
Huge factorial
=EXP(GAMMALN(171)) → 7.26E+306
170 factorial, right at the edge of what a double can hold.
Worth knowing
- LN(n!) = GAMMALN(n+1).
- Log-binomial coefficients: GAMMALN(n+1)-GAMMALN(k+1)-GAMMALN(n-k+1).
- GAMMALN.PRECISE is the same to more decimal places.
Where it goes wrong
- #NUM! for 0 or negative input.
- Exponentiating the result overflows above 171.
Related
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