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In mathematical analysis, factorials are used in power series for the exponential function and other functions, and they also have applications in algebra, number theory, probability theory, and computer science. Much of the mathematics of the factorial function was developed beginning in the late 18th and early 19th centuries.
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
The number of derangements of a set of size n is known as the subfactorial of n or the n th derangement number or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include !n, D n, d n, or n¡ . [a] [1] [2] For n > 0 , the subfactorial !n equals the nearest integer to n!/e, where n!
"Quantitative Estimates for Polynomials in One or Several Variables: From Analysis and Number Theory to Symbolic and Massively Parallel Computation". Mathematics Magazine. 67 (4): 243–257. doi:10.2307/2690843. JSTOR 2690843. {{cite journal}}: CS1 maint: multiple names: authors list (accessible to readers with undergraduate mathematics)
In mathematics, the falling factorial ... this is the number of ways to ... The falling factorial occurs in a formula which represents polynomials using ...
The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS). In this article, a factorial number representation will be flagged by a subscript "!". In addition, some examples will have digits delimited by a colon. For example, 3:4:1:0:1:0! stands for
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
"Stirling_formula", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Peter Luschny, Approximation formulas for the factorial function n! Weisstein, Eric W., "Stirling's Approximation", MathWorld; Stirling's approximation at PlanetMath