Abstract
For interpolatory quadrature rules having abscissas at the zeros of then-th Jacobi polynomialP (α,β) n (x), we show by counterexample that positive Cotes numbers do not exist for all −1<α,β≤3/2.
Zusammenfassung
Durch Gegenbeispiele wird bewiesen, daß nicht für alle Werte α, β mit −1<α,β≤3/2 die Gewichte einer Interpolationsquadratur, deren Knoten die Nullstellen des Jacobipolynomsn-ten GradesP (α,β) n (x) sind, positiv ausfallen.
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Lether, F., Wilhelmsen, D. & Frazier, R. On the positivity of cotes numbers for interpolatory quadratures with Jacobi abscissas. Computing 21, 171–175 (1979). https://doi.org/10.1007/BF02253137
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DOI: https://doi.org/10.1007/BF02253137