Question
One of these objects provides the weight in Gauss–Jacobi quadrature. Sergei Bernstein names a type of these objects that are used to construct a more general class of objects around control points. Before it was generalized by Stone, these objects were doing the "approximation" in the Weierstrass ("VYE-er-stross") approximation theorem. Namesake simple "nodes" characterize examples of these objects named for (*) Chebyshev, which can mitigate Runge's ("ROON-guh's") phenomenon. Barycentric weights define a type of these objects that were used by Lagrange for interpolation. These objects are partial sums of Taylor series. The fundamental theorem of algebra describes the roots of these expressions. For 10 points, name these sums of monomials. ■END■
ANSWER: polynomials [accept cyclotomic polynomials or Bernstein polynomials or Chebyshev polynomials or Chebyshev polynomials of the first kind or Chebyshev polynomials of the second kind] (Bernstein polynomials are used to construct Bézier curves.)
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