ultraspherical abscissa - ορισμός. Τι είναι το ultraspherical abscissa
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Τι (ποιος) είναι ultraspherical abscissa - 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

Gegenbauer polynomials         
  • 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 with ''α''=1
  • Gegenbauer polynomials with ''α''=2
  • Gegenbauer polynomials with ''α''=3
  • An animation showing the polynomials on the ''xα''-plane for the first 4 values of ''n''.
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.
Ordinate         
  • Illustration of a Cartesian coordinate plane, showing the absolute values (unsigned dotted line lengths) of the coordinates of the points (2, 3), (0, 0), (–3, 1), and (–1.5, –2.5). The first value in each of these signed ordered pairs is the abscissa of the corresponding point, and the second value is its ordinate.
NAMES FOR A SYSTEM'S TWO AXES IN COORDINATE GEOMETRY
Ordinate; Abscissæ; Abscissae; Abcissa; Abscissas; Abscissa
·adj Well-ordered; orderly; regular; methodical.
II. Ordinate ·vt To appoint, to regulate; to Harmonize.
III. Ordinate ·noun The distance of any point in a curve or a straight line, measured on a line called the axis of ordinates or on a line parallel to it, from another line called the axis of abscissas, on which the corresponding abscissa of the point is measured.
Abscissas         
  • Illustration of a Cartesian coordinate plane, showing the absolute values (unsigned dotted line lengths) of the coordinates of the points (2, 3), (0, 0), (–3, 1), and (–1.5, –2.5). The first value in each of these signed ordered pairs is the abscissa of the corresponding point, and the second value is its ordinate.
NAMES FOR A SYSTEM'S TWO AXES IN COORDINATE GEOMETRY
Ordinate; Abscissæ; Abscissae; Abcissa; Abscissas; Abscissa
·pl of Abscissa.

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.