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In mathematics, the factorial of a non-negative integer, denoted by !, is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: ! = () = ()! For example, ! =! = =
2.4 Modified-factorial denominators. ... Download as PDF; Printable version; In other projects ... Series (mathematics) List of integrals;
In this article, the symbol () is used to represent the falling factorial, and the symbol () is used for the rising factorial. These conventions are used in combinatorics , [ 4 ] although Knuth 's underline and overline notations x n _ {\displaystyle x^{\underline {n}}} and x n ¯ {\displaystyle x^{\overline {n}}} are increasingly popular.
1. Factorial: if n is a positive integer, n! is the product of the first n positive integers, and is read as "n factorial". 2. Double factorial: if n is a positive integer, n!! is the product of all positive integers up to n with the same parity as n, and is read as "the double factorial of n". 3.
Brocard's problem is a problem in mathematics that seeks integer values of such that ! + is a perfect square, where ! is the factorial. Only three values of n {\displaystyle n} are known — 4, 5, 7 — and it is not known whether there are any more.
This is a list of factorial and binomial topics in mathematics. See also binomial (disambiguation). Abel's binomial theorem; Alternating factorial; Antichain; Beta function; Bhargava factorial; Binomial coefficient. Pascal's triangle; Binomial distribution; Binomial proportion confidence interval; Binomial-QMF (Daubechies wavelet filters ...
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