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The factorial function is a common feature in scientific calculators. [73] It is also included in scientific programming libraries such as the Python mathematical functions module [74] and the Boost C++ library. [75]
In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator), [1]: p.26 is a higher-order function (i.e. a function which takes a function as argument) that returns some fixed point (a value that is mapped to itself) of its argument function, if one exists.
Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning that it is only suitable for integers with specific types of factors; it is the simplest example of an algebraic-group factorisation algorithm.
This latter form is the mathematical definition of factorial as a recurrence relation. Note that the compiler inferred the type of this function to be int -> int , meaning that this function maps ints onto ints.
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. [1] This is in contrast to binary operations, which use two operands. [2] An example is any function : , where A is a set; the function is a unary operation on A.
The rising factorial is also integral to the definition of the hypergeometric function: The hypergeometric function is defined for | | < by the power series (,;;) = = () ()! provided that ,,, …. Note, however, that the hypergeometric function literature typically uses the notation ( a ) n {\displaystyle (a)_{n}} for rising factorials.
The factorial number system is a mixed radix numeral system: the i-th digit from the right has base i, which means that the digit must be strictly less than i, and that (taking into account the bases of the less significant digits) its value is to be multiplied by (i − 1)!
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! = 5×4×3×2×1 = 120. By convention, the value of 0! is defined as 1. This classical factorial function appears prominently in many theorems in number theory. The following are a few of these theorems. [1]