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Coefficient: An expression multiplying one of the monomials of the polynomial. Root (or zero) of a polynomial: Given a polynomial p(x), the x values that satisfy p(x) = 0 are called roots (or zeroes) of the polynomial p. Graphing. End behaviour – Concavity – Orientation – Tangency point – Inflection point – Point where concavity changes.
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory (but not intended to include every mathematical eponym).
Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line; Linear function: First degree polynomial, graph is a straight line. Quadratic function: Second degree polynomial, graph is a parabola.
The most widely used orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special
Pidduck polynomials; Pincherle polynomials; Polylogarithmic function; Polynomial decomposition; Polynomial Diophantine equation; Polynomial evaluation; Polynomial expansion; Polynomial greatest common divisor; Polynomial identity testing; Polynomial interpolation; Polynomial long division; Polynomial matrix; Polynomial matrix spectral ...
Discrete Chebyshev polynomials — polynomials orthogonal with respect to a discrete measure; Favard's theorem — polynomials satisfying suitable 3-term recurrence relations are orthogonal polynomials; Approximation by Fourier series / trigonometric polynomials: Jackson's inequality — upper bound for best approximation by a trigonometric ...
Because of this, expansion of functions in terms of Chebyshev polynomials is sometimes used for polynomial approximations in computer math libraries. Some authors use versions of these polynomials that have been shifted so that the interval of orthogonality is [0, 1] or [−2, 2].