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Τι (ποιος) είναι ultraspherical polynomial - ορισμός
ORTHOGAL POLYNOMIAL SEQUENCE ON THE INTERVAL [−1,1] WITH RESPECT TO THE WEIGHT FUNCTION (1−𝑥²)^{𝛼−½}
Gegenbauer polynomial; Ultraspherical polynomials; Gegenbauer function; Ultraspherical polynomial; Gegenbauer Polynomials; Ultraspherical differential equation; Ultraspherical function
(x) with n=10 and m=1 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=200 "Plot of the Gegenbauer polynomial C n^(m)(x) with n=10 and m=1 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D")
Gegenbauer polynomials
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials.
HOMFLY polynomial
TWO-VARIABLE KNOT POLYNOMIAL, GENERALIZING THE JONES AND ALEXANDER POLYNOMIALS
HOMFLY(PT) polynomial; HOMFLY; LYMPHTOFU polynomial; HOMFLYPT polynomial; Homfly polynomial; FLYPMOTH polynomial; HOMFLY invariant
In the mathematical field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e.
Polynomial transformation
TRANSFORMATION OF A POLYNOMIAL INDUCED BY A TRANSFORMATION OF ITS ROOTS
Transforming Polynomials; Transforming polynomials; Polynomial transformations; Depressed polynomial
In mathematics, a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of a polynomial. Polynomial transformations such as Tschirnhaus transformations are often used to simplify the solution of algebraic equations.
Βικιπαίδεια
Gegenbauer polynomials
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α)
n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer.
