algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial. It is the simplest kind of a sparse polynomial after the...

The binomial theorem can be stated by saying that the polynomial sequence {1, x, x2, x3, ...} is of binomial type. Mathematics portal Binomial approximation...

{\tbinom {n}{k}}.} It is the coefficient of the xk term in the polynomial expansion of the binomial power (1 + x)n; this coefficient can be computed by the multiplicative...

Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients...

3,\ldots \right\}} in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities...

Look up binomial in Wiktionary, the free dictionary. Binomial may refer to: Binomial (polynomial), a polynomial with two terms Binomial coefficient, numbers...

Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes...

i.e., the binomial coefficients. In other words, every integer-valued polynomial can be written as an integer linear combination of binomial coefficients...

scape"), which we know today as Plantago media. Such "polynomial names" may sometimes look like binomials, but are different. For example, Gerard's herbal...

numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician...

word polynomial joins two diverse roots: the Greek poly, meaning "many", and the Latin nomen, or "name". It was derived from the term binomial by replacing...

factor of (n − n). In this case, the series is a finite polynomial, equivalent to the binomial formula. Whether (1) converges depends on the values of...

function, defined as a product of binomial terms corresponding to certain closed walks in a graph. The Martin polynomial, used by Pierre Martin to study...

(absolutely) additive. The polynomial xp is additive. Indeed, for any a and b in the algebraic closure of k one has by the binomial theorem ( a + b ) p = ∑...

number of nonzero terms in a homogeneous polynomial of degree d in n variables). It is equal to the binomial coefficient ( d + n − 1 n − 1 ) = ( d + n...

polynomials that reduces degree by one. The term is due to F. Hildebrandt.) If sn(x) is a Sheffer sequence and pn(x) is the one sequence of binomial type...

one polynomials Appell sequence Askey–Wilson polynomials Bell polynomials Bernoulli polynomials Bernstein polynomial Bessel polynomials Binomial type...

In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series...

of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function...

polynomials Lucas polynomials Spread polynomials Touchard polynomials Rook polynomials Polynomial sequences of binomial type Orthogonal polynomials Secondary...

In combinatorial mathematics, a rook polynomial is a generating polynomial of the number of ways to place non-attacking rooks on a board that looks like...

monomial, binomial, and (less commonly) trinomial; thus x 2 + y 2 {\displaystyle x^{2}+y^{2}} is a "binary quadratic binomial". The polynomial ( y − 3 )...

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...

mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of...

filters) Binomial series Binomial theorem Binomial transform Binomial type Carlson's theorem Catalan number Fuss–Catalan number Central binomial coefficient...

example, 3 × 5 is an integer factorization of 15, and (x − 2)(x + 2) is a polynomial factorization of x2 − 4. Factorization is not usually considered meaningful...

larger positive integer values of n, the correct result is given by the binomial theorem. The name "freshman's dream" also sometimes refers to the theorem...

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...

orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...

interpretation of choosing 0 elements from a set and simplifies polynomial and binomial expansions. However, in other contexts, particularly in mathematical...