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Cited by 3 publications
(4 citation statements)
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“…For Gauss-Radau quadratures with a fixed node at -1, Gautschi in [1] proved that the corresponding kernel for Chebyshev weight functions ω = ω 1 and ω = ω 4 attains its maximum modulus on E ρ on the negative real axis. Recently, Pejčev and Spalević [4] proved and confirmed the empirical results from [1] in the case ω = ω 3 . Milovanović, Spalević and Pranić in [3] also proved and confirmed the empirical results from [1] in the case ω = ω 2 .…”
Section: Introductionmentioning
confidence: 59%
“…For Gauss-Radau quadratures with a fixed node at -1, Gautschi in [1] proved that the corresponding kernel for Chebyshev weight functions ω = ω 1 and ω = ω 4 attains its maximum modulus on E ρ on the negative real axis. Recently, Pejčev and Spalević [4] proved and confirmed the empirical results from [1] in the case ω = ω 3 . Milovanović, Spalević and Pranić in [3] also proved and confirmed the empirical results from [1] in the case ω = ω 2 .…”
Section: Introductionmentioning
confidence: 59%
“…Employing the usual notation a j = 1 2 (ρ j + ρ −j ), j ∈ N and using (7), in conjunction with the identities…”
Section: Maximum Of the Modulus Of Kernel For Gaussian Quadrature Formentioning
confidence: 99%
“…In order to ensure that J 1 is non-negative for each ρ greater than ρ (for each θ ∈ [0, π]), we will use the same method as in the (2.b) in ( [5], p. 19). This method was also used in the purpose of proving the last Gautschi's conjecture ( [7]). Hence, the method we will use in this case is to find the minimal ρ such that if we rewrite the polynomial J 1 (ρ) as a polynomial in ρ − ρ , then all of its coefficients (depending only on θ when we fix ρ ) are non-negative for all θ ∈ [0, π].…”
Section: The Determination Of ρ Minmentioning
confidence: 99%
“…Poslednja preostala hipoteza je kompletno dokazana u ovoj disertaciji. Dokaz je u obliku rada prihva en za xtampu u qasopisu Applied Mathematics and Computation ( [57]).…”
Section: Organizacija Disertacije Po Poglavljimaunclassified