In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to...

Sheffer sequence or poweroid is a polynomial sequence, i.e., a sequence (pn(x) : n = 0, 1, 2, 3, ...) of polynomials in which the index of each polynomial equals...

In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence { p n ( x ) } n = 0 , 1 , 2 , … {\displaystyle \{p_{n}(x)\}_{n=0...

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

function. They are an Appell sequence (i.e. a Sheffer sequence for the ordinary derivative operator). For the Bernoulli polynomials, the number of crossings...

In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers { 0 , 1 , 2 , 3 , … } {\textstyle \left\{0,1,2...

mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other...

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)}...

In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling...

the Fibonacci polynomials are a polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in...

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

\int _{0}^{\infty }f(x)e^{-x}\,dx.} These polynomials, usually denoted L0, L1, ..., are a polynomial sequence which may be defined by the Rodrigues formula...

of the sequence starting with any seed other than 22. Conway's constant is the unique positive real root of the following polynomial (sequence A137275...

polynomials Chebyshev polynomials Difference polynomials Generalized Appell polynomials q-difference polynomials Other sequences generated by more complex...

coefficient is a polynomial in the cumulants; these are the Bell polynomials, named after Eric Temple Bell.[citation needed] This sequence of polynomials is of binomial...

In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike...

Touchard polynomials, studied by Jacques Touchard (1939), also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial...

abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous...

orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as...

example, the polynomial corresponding to Figure 1 is x 4 + x + 1 {\displaystyle x^{4}+x+1} . A necessary and sufficient condition for the sequence generated...

sequence whose terms are integers. A polynomial sequence is a sequence whose terms are polynomials. A positive integer sequence is sometimes called multiplicative...

the generator polynomial x + 1 (two terms), and has the name CRC-1. A CRC-enabled device calculates a short, fixed-length binary sequence, known as the...

Examples of such sequences are 1, 0, 0, 0, ... (order 1) and 1, 6, 6, 6, ... (order 2).[citation needed] A sequence defined by a polynomial s n = a 0 + a...

In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α) n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight...

delta operator Q {\displaystyle Q} has a unique sequence of "basic polynomials", a polynomial sequence defined by three conditions: p 0 ( x ) = 1 ; {\displaystyle...

In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are...

In mathematics, the Sturm sequence of a univariate polynomial p is a sequence of polynomials associated with p and its derivative by a variant of Euclid's...

combinatorial mathematics, the q-difference polynomials or q-harmonic polynomials are a polynomial sequence defined in terms of the q-derivative. They...

value x, the result is the sequence of Fibonacci polynomials. Not adding the immediately preceding numbers. The Padovan sequence and Perrin numbers have...

function is convergent, its sum is the limit of the infinite sequence of the Taylor polynomials. A function may differ from the sum of its Taylor series,...