# Definition of factorial in English:

## factorial

### Pronunciation /fakˈtôrēəl//fækˈtɔriəl/

Translate factorial into Spanish

### noun

• 1

(also !)
Mathematics
The product of an integer and all the integers below it; e.g. factorial four (4!) is equal to 24.

‘The gamma function is undefined for zero and negative integers, from which we can conclude that factorials of negative integers do not exist.’
• ‘Stirling wrote to De Moivre pointing out some errors that he had made in a table of logarithms of factorials in the book.’
• ‘They learned of each other's discoveries because each of them communicated his work to James Stirling, whose approximation for the factorial is a special case of the Euler-Maclaurin summation.’
• ‘Now Stirling's formula is a classical approximation for the factorial function, and factorials are one way to evaluate binomial coefficients.’
• ‘The experiment was a completely randomized design, with eight treatment combinations, forming a 4 x 2 factorial (four clones and two watering regimes) with five plants in individual pots per treatment combination as replication.’
1. 1.1The product of a series of factors in an arithmetic progression.
‘In the proof below, we use the fact that e is the sum of the series of inverted factorials.’
• ‘‘A factorial is the product of consecutive numbers from 1 to that particular digit and is represented by placing a‘!’’