List of factorial and binomial topics
Encyclopedia
This is a list of factorial and binomial topics in mathematics
, by Wikipedia page. See also binomial (disambiguation)
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, by Wikipedia page. See also binomial (disambiguation)
Binomial (disambiguation)
A binomial is a polynomial with two terms.Binomial may also refer to:In mathematics:*Binomial theorem, a theorem about powers of binomials*Binomial coefficient, numbers appearing in the expansions of powers of binomials...
.
- Abel's binomial theorem
- Alternating factorialAlternating factorialIn mathematics, an alternating factorial is the absolute value of the alternating sum of the first n factorials.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...
- AntichainAntichainIn mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable. Let S be a partially ordered set...
- Beta function
- Binomial coefficientBinomial coefficientIn mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written \tbinom nk , and it is the coefficient of the x k term in...
- Binomial distribution
- Binomial proportion confidence intervalBinomial proportion confidence intervalIn statistics, a binomial proportion confidence interval is a confidence interval for a proportion in a statistical population. It uses the proportion estimated in a statistical sample and allows for sampling error. There are several formulas for a binomial confidence interval, but all of them rely...
- Binomial-QMFBinomial-QMFOrthonormal binomial quadrature mirror filter bank with perfect reconstruction was designed by Ali Akansu, et al. published in 1990 using the family of binomial polynomials for subband decomposition of discrete-time signals....
(Daubechies wavelet filters) - Binomial seriesBinomial seriesIn mathematics, the binomial series is the Taylor series at x = 0 of the function f given by f = α, where is an arbitrary complex number...
- Binomial theoremBinomial theoremIn elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with , and the coefficient a of...
- Pascal's trianglePascal's triangleIn mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...
- Pascal's triangle
- Binomial transform
- Binomial type
- Carlson's theoremCarlson's theoremIn mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem about a summable expansion of an analytic function. It is typically invoked to defend the uniqueness of a Newton series expansion. Carlson's theorem has generalized analogues for expansions in other bases of...
- Catalan numberCatalan numberIn combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involvingrecursively defined objects...
- Central binomial coefficientCentral binomial coefficientIn mathematics the nth central binomial coefficient is defined in terms of the binomial coefficient byThey are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle...
- CombinationCombinationIn mathematics a combination is a way of selecting several things out of a larger group, where order does not matter. In smaller cases it is possible to count the number of combinations...
- De Polignac's formulaDe Polignac's formulaIn number theory, de Polignac's formula, named after Alphonse de Polignac, gives the prime decomposition of the factorial n!, where n ≥ 1 is an integer. L. E. Dickson attributes the formula to Legendre.-The formula:...
- Difference operator
- Difference polynomials
- Digamma function
- Erdős–Ko–Rado theoremErdos–Ko–Rado theoremIn combinatorics, the Erdős–Ko–Rado theorem of Paul Erdős, Chao Ko, and Richard Rado is a theorem on hypergraphs, specifically, on uniform hypergraphs of rank r.The theorem is as follows...
- Euler–Mascheroni constantEuler–Mascheroni constantThe Euler–Mascheroni constant is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter ....
- Faà di Bruno's formulaFaà di Bruno's formulaFaà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named after , though he was not the first to state or prove the formula...
- FactorialFactorialIn 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...
- Factorial moment
- Factorial primeFactorial primeA factorial prime is a prime number that is one less or one more than a factorial . The first few factorial primes are:n! − 1 is prime for :n! + 1 is prime for :...
- Gamma distribution
- Gamma functionGamma functionIn mathematics, the gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers...
- Gaussian binomial coefficient
- Hyperfactorial
- Hypergeometric distribution
- Hypergeometric function identities
- Hypergeometric seriesHypergeometric seriesIn mathematics, a generalized hypergeometric series is a series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by...
- Incomplete beta function
- Incomplete gamma functionIncomplete gamma functionIn mathematics, the gamma function is defined by a definite integral. The incomplete gamma function is defined as an integral function of the same integrand. There are two varieties of the incomplete gamma function: the upper incomplete gamma function is for the case that the lower limit of...
- Lah numberLah numberIn mathematics, Lah numbers, discovered by Ivo Lah in 1955, are coefficients expressing rising factorials in terms of falling factorials.Unsigned Lah numbers have an interesting meaning in combinatorics: they count the number of ways a set of n elements can be partitioned into k nonempty linearly...
- Lanczos approximation
- Lozanić's triangleLozanic's triangleLozanić's triangle is a triangular array of binomial coefficients in a manner very similar to that of Pascal's triangle...
- Mahler's theoremMahler's theoremIn mathematics, Mahler's theorem, introduced by , expresses continuous p-adic functions in terms of polynomials.In any field, one has the following result. Let=f-f\,be the forward difference operator...
- Multinomial distribution
- Multinomial coefficient, Multinomial formula, Multinomial theoremMultinomial theoremIn mathematics, the multinomial theorem says how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem to polynomials.-Theorem:...
- Multiplicities of entries in Pascal's triangleMultiplicities of entries in Pascal's triangleIn combinatorial number theory, Singmaster's conjecture, named after David Singmaster, says there is a finite upper bound on the multiplicities of entries in Pascal's triangle...
- MultisetMultisetIn mathematics, the notion of multiset is a generalization of the notion of set in which members are allowed to appear more than once...
- Multivariate gamma functionMultivariate gamma functionIn mathematics, the multivariate Gamma function, Γp, is a generalization of the Gamma function. It is useful in multivariate statistics, appearing in the probability density function of the Wishart and Inverse Wishart distributions....
- Narayana numbers
- Negative binomial distributionNegative binomial distributionIn probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of Bernoulli trials before a specified number of failures occur...
- Nörlund–Rice integral
- Pascal matrixPascal matrixIn mathematics, particularly matrix theory and combinatorics, the Pascal matrix is an infinite matrix containing the binomial coefficients as its elements. There are three ways to achieve this: as either an upper-triangular matrix, a lower-triangular matrix, or a symmetric matrix...
- Pascal's pyramidPascal's pyramidIn mathematics, Pascal's Pyramid is a three-dimensional arrangement of the trinomial numbers, which are the coefficients of the trinomial expansion and the trinomial distribution. Pascal's Pyramid is the three-dimensional analog of the two-dimensional Pascal's triangle, which contains the binomial...
- Pascal's simplexPascal's simplexIn mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem.- Induction of Pascal's simplices :...
- Pascal's trianglePascal's triangleIn mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...
- PermutationPermutationIn mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
- Pochhammer symbolPochhammer symbolIn mathematics, the Pochhammer symbol introduced by Leo August Pochhammer is the notation ', where is a non-negative integer. Depending on the context the Pochhammer symbol may represent either the rising factorial or the falling factorial as defined below. Care needs to be taken to check which...
(also falling, lower, rising, upper factorials) - Poisson distributionPoisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...
- Polygamma function
- PrimorialPrimorialIn 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 multiplying successive positive integers, only successive prime numbers are multiplied...
- Proof of Bertrand's postulate
- Sierpinski triangleSierpinski triangleThe Sierpinski triangle , also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915. However, similar patterns appear already in the 13th-century Cosmati mosaics in the cathedral...
- Star of David theoremStar of David theoremThe Star of David theorem is a mathematical result on arithmetic properties of binomial coefficients. It was discovered by H.W. Gould in 1972.- Statement :...
- Stirling numberStirling numberIn mathematics, Stirling numbers arise in a variety of combinatorics problems. They are named after James Stirling, who introduced them in the 18th century. Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second...
- Stirling transform
- Stirling's approximationStirling's approximationIn mathematics, Stirling's approximation is an approximation for large factorials. It is named after James Stirling.The formula as typically used in applications is\ln n! = n\ln n - n +O\...
- Subfactorial
- Table of Newtonian series
- Taylor seriesTaylor seriesIn mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....
- Trinomial expansion
- Vandermonde's identity
- Wilson primeWilson primeA Wilson prime, named after English mathematician John Wilson, is a prime number p such that p2 divides ! + 1, where "!" denotes the factorial function; compare this with Wilson's theorem, which states that every prime p divides ! + 1.The only known Wilson primes are 5, 13, and...
- Wilson's theorem
- Wolstenholme primeWolstenholme primeIn number theory, a Wolstenholme prime is a special type of prime number satisfying a stronger version of Wolstenholme's theorem. Wolstenholme's theorem is a congruence relation satisfied by all prime numbers greater than 7...