# Definition of factorial in English:

## factorial

Pronunciation: /fakˈtôrēəl/

## noun

Mathematics
1The product of an integer and all the integers below it; e.g., factorial four (4!) is equal to 24. (Symbol: !)
Example sentences
• 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.
1.1The product of a series of factors in an arithmetic progression.
Example sentences
• 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‘!’

chiefly Mathematics
Relating to a factor or factorial: a factorial design
More example sentences
• Experimental designs involving factorial combination of multiple independent variables call for some inventiveness when it comes to graphical presentation of data.
• Around 1926, a British statistician, Ronald Fisher, while working in the field of agriculture, developed a new form of experimentation called two-level factorial design.
• A 2 x 4 x 12 factorial design was used to assess the effects of light, temperature and month, respectively, on the germination of Spergularia marina seeds.

## Derivatives

#### factorially

Example sentences
• Three stimulus frequencies were combined factorially with two input channels (left and right ears) and three measurement procedures.
• The investigation of factorially simple tasks, which are not especially cognitively demanding, has prompted hopes of arriving at a definition of intelligence that is both precise and explanatory.
• The shortened 18-item scale is both more reliable and more factorially pure than the original 25-item measure with which it correlates at a.93 level.

Syllabification: fac·to·ri·al

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