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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, ! =! = =
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,
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
Let be a natural number. For a base >, we define the sum of the factorials of the digits [5] [6] of , :, to be the following: = =!. where = ⌊ ⌋ + is the number of digits in the number in base , ! is the factorial of and
Comparison of Stirling's approximation with the factorial In mathematics , Stirling's approximation (or Stirling's formula ) is an asymptotic approximation for factorials . It is a good approximation, leading to accurate results even for small values of n {\displaystyle n} .
The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages.
In mathematics, a pseudogamma function is a function that interpolates the factorial. The gamma function is the most famous solution to the problem of extending the notion of the factorial beyond the positive integers only. However, it is clearly not the only solution, as, for any set of points, an infinite number of curves can be drawn through ...
In mathematics, an alternating factorial is the absolute value of the alternating sum of the first n factorials of positive integers.. This is the same as their sum, with the odd-indexed factorials multiplied by −1 if n is even, and the even-indexed factorials multiplied by −1 if n is odd, resulting in an alternation of signs of the summands (or alternation of addition and subtraction ...