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Much of the mathematics of the factorial function was developed beginning in the late 18th and early 19th centuries. Stirling's approximation provides an accurate approximation to the factorial of large numbers, showing that it grows more quickly than exponential growth.
In mathematics, the Fibonorial n! F, also called the Fibonacci factorial, where n is a nonnegative integer, is defined as the product of the first n positive Fibonacci numbers, i.e. !:= =,, where F i is the i th Fibonacci number, and 0!
Download as PDF; Printable version; ... Factorial moment generating function; Factorial number system; ... Telephone number (mathematics)
Catalan number. Fuss–Catalan number; Central binomial coefficient; Combination; Combinatorial number system; De Polignac's formula; Difference operator; Difference polynomials; Digamma function; Egorychev method; Erdős–Ko–Rado theorem; Euler–Mascheroni constant; Faà di Bruno's formula; Factorial; Factorial moment; Factorial number ...
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
The ratio of the factorial!, that counts all permutations of an ordered set S with cardinality, and the subfactorial (a.k.a. the derangement function) !, which counts the amount of permutations where no element appears in its original position, tends to as grows.
mXparser is an open-source mathematical expressions parser/evaluator providing abilities to calculate various expressions at a run time. [1] Expressions definitions are given as plain text, then verified in terms of grammar / syntax, finally calculated.
In mathematics, the Jordan–Pólya numbers are the numbers that can be obtained by multiplying together one or more factorials, not required to be distinct from each other. For instance, 480 {\displaystyle 480} is a Jordan–Pólya number because 480 = 2 ! ⋅ 2 ! ⋅ 5 ! {\displaystyle 480=2!\cdot 2!\cdot 5!} .