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function, where g and h are coprime polynomials. The polynomial transformation of a polynomial P by f is the polynomial Q (defined up to the product by a...

polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis...

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

polynomials, quadratic polynomials and cubic polynomials. For higher degrees, the specific names are not commonly used, although quartic polynomial (for...

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

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

Chebyshev polynomial basis. Like the Chebyshev polynomials, it is named after Pafnuty Chebyshev. The two most common types of discrete Chebyshev transforms use...

of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more...

basis for polynomials. In the complex case the trigonometric polynomials are spanned by the positive and negative powers of eix, Laurent polynomials in z under...

elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed...

a recursive factorization of the polynomial z n − 1 {\displaystyle z^{n}-1} , here into real-coefficient polynomials of the form z m − 1 {\displaystyle...

generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor...

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...

by transforming or reducing it to inputs for the second problem and calling the subroutine one or more times. If both the time required to transform the...

_{n}\left(2x{\sqrt {\pi }}\right),} where Hen(x) are the "probabilist's" Hermite polynomials, defined as H e n ( x ) = ( − 1 ) n e 1 2 x 2 ( d d x ) n e − 1 2 x 2...

equations into algebraic polynomial equations, and by simplifying convolution into multiplication. Once solved, the inverse Laplace transform reverts to the original...

polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials. The original use of interpolation polynomials was...

the Kravchuk polynomials (Atakishiyev and Wolf, 1997). The "best" choice of eigenvectors to define a fractional discrete Fourier transform remains an open...

k at a time to repeatedly produce potential polynomials, until a sufficient number of matching polynomials are produced to reasonably eliminate any errors...

not sufficient. Just as stable polynomials are crucial for assessing the stability of systems described by polynomials, stability matrices play a vital...