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# Factorial

In mathematics, 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, The value of 0! is 1, according to the convention for an empty product. [1]

126 relations: Algebra, Alternating factorial, Analytic function, Ancient Society of College Youths, Arbitrary-precision arithmetic, Average, Big O notation, Binary logarithm, Binary tree, Binomial coefficient, Binomial theorem, Bohr–Mollerup theorem, Calculator, Calculus, Carl Friedrich Gauss, Catalan number, Change ringing, Christian Kramp, Clifford A. Pickover, Combination, Combinatorics, Common logarithm, Comparison sort, Complete graph, Complex number, Composite number, Computational complexity theory, Computer algebra system, Concrete Mathematics, Continued fraction, Convergent series, Derangement, Derivative, Determinant, Digamma function, Dimension, Divide and conquer algorithms, Double exponential function, E (mathematical constant), Empty product, Empty set, Entire function, Enumerative combinatorics, Euler–Mascheroni constant, Exponential factorial, Exponential function, Exponential growth, Exponentiation, Fabian Stedman, Factorial number system, ... Expand index (76 more) »

## Algebra

Algebra (from Arabic and Farsi "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

## Alternating factorial

In mathematics, an alternating factorial is the absolute value of the alternating sum of the first n factorials of positive integers.

## Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

## Ancient Society of College Youths

The Ancient Society of College Youths (ASCY) is the world's premier society of church bellringers, founded in 1637 and based in the City of London.

## Arbitrary-precision arithmetic

In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system.

## Average

In colloquial language, an average is the sum of a list of numbers divided by the number of numbers in the list.

## Big O notation

In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions.

## Binary logarithm

In mathematics, the binary logarithm is the logarithm to the 2.

## Binary tree

In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child.

## Binomial coefficient

In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem.

## Binomial theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

## Bohr–Mollerup theorem

In mathematical analysis, the Bohr–Mollerup theorem is a theorem named after the Danish mathematicians Harald Bohr and Johannes Mollerup, who proved it.

## Calculator

An electronic calculator is a small, portable electronic device used to perform both basic operations of arithmetic and complex mathematical operations.

## Calculus

Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

## Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß,; Carolus Fridericus Gauss) (30 April 177723 February 1855) was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, astronomy, matrix theory, and optics.

## Catalan number

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects.

## Change ringing

Change ringing is the art of ringing a set of tuned bells in a series of mathematical patterns called "changes".

## Christian Kramp

Christian Kramp (8 July 1760 – 13 May 1826) was a French mathematician, who worked primarily with factorials.

## Clifford A. Pickover

Clifford Alan Pickover (born August 15, 1957) is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity and is employed at the IBM Thomas J. Watson Research Center in Yorktown, New York.

## Combination

In mathematics, a combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter.

## Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

## Common logarithm

In mathematics, the common logarithm is the logarithm with base 10.

## Comparison sort

A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list.

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## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers and is the imaginary unit, that satisfies the equation.

## Composite number

A composite number is a positive integer that has at least one positive divisor other than one or the number itself.

## Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

## Computer algebra system

A computer algebra system (CAS) is a software program that allows computation over mathematical expressions in a way which is similar to the traditional manual computations of mathematicians and scientists.

## Concrete Mathematics

Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik, is a textbook that is widely used in computer-science departments.

## Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

## Convergent series

In mathematics, a series is the sum of the terms of a sequence of numbers.

## Derangement

In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position.

## Derivative

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable).

## Determinant

In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix.

## Digamma function

In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: It is the first of the polygamma functions.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Divide and conquer algorithms

In computer science, divide and conquer (D&amp;C) is an algorithm design paradigm based on multi-branched recursion.

## Double exponential function

A double exponential function is a constant raised to the power of an exponential function.

## E (mathematical constant)

The number is an important mathematical constant that is the base of the natural logarithm.

## Empty product

In mathematics, an empty product, or nullary product, is the result of multiplying no factors.

## Empty set

In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

## Entire function

In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane.

## Enumerative combinatorics

Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed.

## Euler–Mascheroni constant

The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (\gamma).

## Exponential factorial

An exponential factorial is a positive integer n raised to the power of n &minus; 1, which in turn is raised to the power of n &minus; 2, and so on and so forth, that is, The exponential factorial can also be defined with the recurrence relation The first few exponential factorials are 1, 1, 2, 9, 262144, etc.

## Exponential function

In mathematics, an exponential function is a function of the form The input variable x occurs as an exponent – hence the name.

## Exponential growth

Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value.

## Exponentiation

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: In that case, bn is called the n-th power of b, or b raised to the power n. The exponent is usually shown as a superscript to the right of the base.

## Fabian Stedman

Fabian Stedman (b. Yarkhill, Herefordshire 1640, d. 1713) was a leading figure in campanology and bell-ringing.

## Factorial number system

In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations.

## Factorial prime

A factorial prime is a prime number that is one less or one more than a factorial (all factorials > 1 are even).

## Factorion

A factorion is a natural number that equals the sum of the factorials of its decimal digits.

## Floating point

In computing, floating point is the formulaic representation which approximates a real number so as to support a trade-off between range and precision.

## Floor and ceiling functions

In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively.

## Fraction (mathematics)

A fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

## Functional equation

In mathematics, a functional equation is any equation that specifies a function in implicit form.

## Gamma function

In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

## Generating primes

In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently.

## Glaisher–Kinkelin constant

In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted A, is a mathematical constant, related to the K-function and the Barnes G-function.

## GNU Multiple Precision Arithmetic Library

The GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating point numbers.

## Googol

A googol is the large number 10100.

## Half-integer

In mathematics, a half-integer is a number of the form where n is an integer.

## Hypersphere

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## Integral

The integral is an important concept in mathematics.

## Irrational number

In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers.

## Irrationality sequence

In mathematics, a sequence of positive integers an is called an irrationality sequence if it has the property that, for every sequence xn of positive integers, the sum of the series exists (that is, it converges) and is an irrational number.

Jacques Salomon Hadamard ForMemRS (8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.

## K-function

In mathematics, the K-function, typically denoted K(z), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of the factorial to the Gamma function.

## Knuth's up-arrow notation

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.

## Legendre's formula

In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!.

## Leonhard Euler

Leonhard Euler (17071783) was a pioneering Swiss mathematician and physicist.

## Linear function

In mathematics, the term linear function refers to two distinct, although related, notions.

## List of factorial and binomial topics

This is a list of factorial and binomial topics in mathematics, by Wikipedia page.

## List of integrals of trigonometric functions

The following is a list of integrals (antiderivative functions) of trigonometric functions.

## Logarithmically convex function

In mathematics, a function f defined on a convex subset of a real vector space and taking positive values is said to be logarithmically convex or superconvex if \circ f, the composition of the logarithmic function with f, is a convex function.

## Maple (software)

Maple is a commercial computer algebra system developed and sold commercially by Maplesoft, a software company based in Waterloo, Ontario, Canada.

## Matching (graph theory)

In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.

## Mathematica

Mathematica is a computational software program used in many scientific, engineering, mathematical and computing fields, based on symbolic mathematics.

## Mathematical analysis

Mathematical analysis is a branch of mathematics that studies continuous change and includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions.

## Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas.

## Mathematical software

Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.

## Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

## Meromorphic function

In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points (the poles of the function), at each of which the function must have a Laurent series.

## Multiplication algorithm

A multiplication algorithm is an algorithm (or method) to multiply two numbers.

## Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x&minus;1, is a number which when multiplied by x yields the multiplicative identity, 1.

## N-sphere

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.

## Natural logarithm

The natural logarithm of a number is its logarithm to the base e, where ''e'' is an irrational and transcendental constant approximately equal to.

## Natural number

In mathematics, the natural numbers (sometimes called the whole numbers): "whole number An integer, though sometimes it is taken to mean only non-negative integers, or just the positive integers." give definitions of "whole number" under several headwords: INTEGER … Syn. whole number.

## Neil Sloane

Neil James Alexander Sloane (born October 10, 1939) is a British-U.S. mathematician.

## Number theory

Number theory (or arithmeticEspecially in older sources; see two following notes.) is a branch of pure mathematics devoted primarily to the study of the integers.

## Operator (mathematics)

An operator is a mapping from one vector space or module to another.

## Parity (mathematics)

Parity is a mathematical term that describes the property of an integer's inclusion in one of two categories: even or odd.

## Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

## Personal computer

A personal computer is a general-purpose computer whose size, capabilities and original sale price make it useful for individuals, and is intended to be operated directly by an end-user with no intervening computer operator.

## Peter Borwein

Peter Benjamin Borwein (born St. Andrews, Scotland, May 10, 1953) is a Canadian mathematician and a professor at Simon Fraser University.

## Pochhammer symbol

In mathematics, the Pochhammer symbol introduced by Leo August Pochhammer is the notation, where is a non-negative integer.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

## Power rule

In calculus, the power rule is one of the most important differentiation rules.

## Prime number

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

## Primorial

In mathematics, and more particularly in number theory, primorial is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, only prime numbers are multiplied.

## Probability theory

Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena.

## Product (mathematics)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.

## Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

## Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function, ζ(s), is a function of a complex variable s that analytically continues the sum of the infinite series which converges when the real part of s is greater than 1.

## SageMath

SageMath (previously Sage or SAGE, System for Algebra and Geometry Experimentation) is mathematical software with features covering many aspects of mathematics, including algebra, combinatorics, numerical mathematics, number theory, and calculus.

## Schönhage–Strassen algorithm

The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers.

## Scientific notation

Scientific notation (also referred to as "standard form" or "standard index form") is a way of expressing numbers that are too big or too small to be conveniently written in decimal form and is commonly used by scientists, mathematicians and engineers.

## Sequence

In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed.

## Series (mathematics)

A series is, informally speaking, the sum of the terms of a sequence.

## Shannon number

The Shannon number, named after Claude Shannon, is an estimated lower bound on the game-tree complexity of chess of 10120, based on about 103 initial moves for White and Black and a typical game lasting about 40 pairs of moves.

## Simon Plouffe

Simon Plouffe (born June 11, 1956, Saint-Jovite, Quebec) is a mathematician who discovered the formula for the BBP algorithm (the Bailey–Borwein–Plouffe formula) which permits the computation of the nth binary digit of &pi;, in 1995.

## Sorting algorithm

A sorting algorithm is an algorithm that puts elements of a list in a certain order.

Springer Science+Business Media or Springer is a global publishing company that publishes books, e-books and peer-reviewed journals in science, technical and medical (STM) publishing.

## Srinivasa Ramanujan

Srinivasa Ramanujan Iyengar (22 December 188726 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions.

## Stirling's approximation

In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials.

## Symmetrization

In mathematics, symmetrization is a process that converts any function in n variables to a symmetric function in n variables.

## Taylor's theorem

In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial.

## Tetration

In mathematics, tetration (or hyper-4) is the next hyperoperator after exponentiation, and is defined as iterated exponentiation.

## Thomas Joannes Stieltjes

Thomas Joannes Stieltjes (29 December 1856 – 31 December 1894) was a Dutch mathematician.

## Trailing zero

In mathematics, trailing zeros are a sequence of 0s in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow.

## Triangular number

A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right.

## Vandermonde matrix

In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row, i.e., an m &times; n matrix 1 & \alpha_1 & \alpha_1^2 & \dots & \alpha_1^\\ 1 & \alpha_2 & \alpha_2^2 & \dots & \alpha_2^\\ 1 & \alpha_3 & \alpha_3^2 & \dots & \alpha_3^\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & \alpha_m & \alpha_m^2 & \dots & \alpha_m^ \end or for all indices i and j. (Some authors use the transpose of the above matrix.) The determinant of a square Vandermonde matrix (where m.

## Volume

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

## Wilson's theorem

In number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if That is, it asserts that the factorial (n - 1)!.

## Wolfram Alpha

Wolfram Alpha (also styled WolframAlpha and Wolfram|Alpha) is a computational knowledge engine or answer engine developed by Wolfram Research.

## References

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