ultraspherical function - translation to ρωσικά
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ultraspherical function - translation to ρωσικά

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

ultraspherical function         
  • 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''.

математика

ультрасферическая функция

ultraspherical polynomial         
  • 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''.

математика

ультрасферический многочлен

многочлен Гегенбауэра

function of several variables         
  • A binary operation is a typical example of a bivariate function which assigns to each pair <math>(x, y)</math> the result <math>x\circ y</math>.
  • A function that associates any of the four colored shapes to its color.
  • Together, the two square roots of all nonnegative real numbers form a single smooth curve.
  • Graph of a linear function
  • The function mapping each year to its US motor vehicle death count, shown as a [[line chart]]
  • The same function, shown as a bar chart
  • Graph of a polynomial function, here a quadratic function.
  • Graph of two trigonometric functions: [[sine]] and [[cosine]].
  • right
ASSOCIATION OF A SINGLE OUTPUT TO EACH INPUT
Mathematical Function; Mathematical function; Function specification (mathematics); Mathematical functions; Empty function; Function (math); Ambiguous function; Function (set theory); Function (Mathematics); Functions (mathematics); Domain and range; Functional relationship; G(x); H(x); Function notation; Output (mathematics); Ƒ(x); Overriding (mathematics); Overriding union; F of x; Function of x; Bivariate function; Functional notation; Function of several variables; Y=f(x); ⁡; Draft:The Repeating Fractional Function; Image (set theory); Mutivariate function; Draft:Specifying a function; Function (maths); Functions (math); Functions (maths); F(x); Empty map; Function evaluation
функция нескольких переменных

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.

Μετάφραση του &#39ultraspherical function&#39 σε Ρωσικά