In mathematics, Zolotarev polynomials are polynomials used in approximation theory. They are sometimes used as an alternative to the Chebyshev polynomials where accuracy of approximation near the origin is of less importance. Zolotarev polynomials differ from the Chebyshev polynomials in that two of the coefficients are fixed in advance rather than allowed to take on any value. The Chebyshev polynomials of the first kind are a special case of Zolotarev polynomials. These polynomials were introduced by Russian mathematician Yegor Ivanovich Zolotarev in 1868.
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mathematics, Zolotarevpolynomials are polynomials used in approximation theory. They are sometimes used as an alternative to the Chebyshev polynomials where...
Appliquées. 3e Série. 6: 51–84, 129–166. Zolotarev's lemma Zolotarevpolynomials Elliptic filter also known as a Zolotarev filter. "Andrei Kolmogorov - the Mathematics...
it is elementary), but the strict proof for it was ultimately done by Zolotarev. The following is a more complex example that involves both algebraic...
weak law of large numbers), the Bertrand–Chebyshev theorem, Chebyshev polynomials, Chebyshev linkage, and Chebyshev bias. The surname Chebyshev has been...
as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a signal processing filter with equalized ripple (equiripple)...
a solution in time polynomial in the lattice dimension. For smaller values γ {\displaystyle \gamma } , the Block Korkine-Zolotarev algorithm (BKZ) is...
uncountably infinite. Since the polynomials with rational coefficients are countable, and since each such polynomial has a finite number of zeroes, the...
order of permutations Wreath product Young symmetrizer Zassenhaus group Zolotarev's lemma Burnside ring Conditionally convergent series Riemann series theorem...
non-squares, it can be uniformly interpreted as the sign of a permutation by Zolotarev's lemma. The Jacobi symbol (a/n) is a Dirichlet character to the modulus...
a generalized sign map. The fifteen puzzle is a classic application Zolotarev's lemma Jacobson (2009), p. 50. Rotman (1995), p. 9, Theorem 1.6. Jacobson...
and proved it in 1927. Dedekind zeta function Rational reciprocity law Zolotarev's lemma Gauss, DA § 4, arts 107–150 E.g. in his mathematical diary entry...
12942/lrr-2013-4. PMC 5255893. PMID 28179843. Uchaikin, Vladimir V.; Zolotarev, Vladimir M. (1999). Chance and Stability: Stable Distributions and their...
counting. One by Gotthold Eisenstein counts lattice points. Another applies Zolotarev's lemma to ( Z / p q Z ) × {\displaystyle (\mathbb {Z} /pq\mathbb {Z} )^{\times...
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