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1The product of an integer and all the integers below it; e.g. factorial four (4!) is equal to 24.
‘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.’
‘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.’
‘Stirling wrote to De Moivre pointing out some errors that he had made in a table of logarithms of factorials in the book.’
‘The gamma function is undefined for zero and negative integers, from which we can conclude that factorials of negative integers do not exist.’
‘Now Stirling's formula is a classical approximation for the factorial function, and factorials are one way to evaluate binomial coefficients.’
1.1The product of a series of factors in an arithmetical progression.
‘‘A factorial is the product of consecutive numbers from 1 to that particular digit and is represented by placing a‘!’’
‘In the proof below, we use the fact that e is the sum of the series of inverted factorials.’
adjective
Mathematics
Relating to a factor or factorial:
‘a factorial design’
‘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.’
‘Our trial was of factorial design in order to compare three types of treatment within a single trial, in order to derive the maximum amount of data from the minimum number of patients.’
‘One possible approach to make this search more systematic is the use of factorial design, which involves a set of experiments intended to identify important effects and interactions.’
‘Experimental designs involving factorial combination of multiple independent variables call for some inventiveness when it comes to graphical presentation of data.’