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The word "factorial" (originally French: factorielle) was first used in 1800 by Louis François Antoine Arbogast, [18] in the first work on Faà di Bruno's formula, [19] but referring to a more general concept of products of arithmetic progressions. The "factors" that this name refers to are the terms of the product formula for the factorial. [20]
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The falling factorial can be extended to real values of using the gamma function provided and + are real numbers that are not negative integers: = (+) (+) , and so can the rising factorial: = (+) . Calculus
These are counted by the double factorial 15 = (6 − 1)‼. In mathematics, the double factorial of a number n, denoted by n‼, is the product of all the positive integers up to n that have the same parity (odd or even) as n. [1] That is,
Consider the factorial function F(n) recursively defined by F(n) = 1, if n = 0; else n × F(n − 1). In the lambda expression which is to represent this function, a parameter (typically the first one) will be assumed to receive the lambda expression itself as its value, so that calling it – applying it to an argument – will amount to ...
When an inline formula is long enough, it can be helpful to allow it to break across lines. Whether using LaTeX or templates, split the formula at each acceptable breakpoint into separate <math> tags or {} templates with any binary relations or operators and intermediate whitespace included at the trailing rather than leading end of a part.
In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!. It is named after Adrien-Marie Legendre . It is also sometimes known as de Polignac's formula , after Alphonse de Polignac .