ISSN:
0945-3245
Schlagwort(e):
AMS(MOS): 65D30
;
CR: 5.16
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Summary Let $$f(z) = \sum\limits_{j = 0}^\infty {t_{2j} z^{2j} } ,t_{2j} \geqq 0(j = 0,1,2,...)$$ , be holomorphic in an open disc with the centrez 0=0 and radiusr〉1. LetQ n (n=1, 2, ...) be interpolatory quadrature formulas approximating the integral $$\int\limits_{ - 1}^{ + 1} {f(x)dx} $$ . In this paper some classes of interpolatory quadratures are considered, which are based on the zeros of orthogonal polynomials corresponding to an even weight function. It is shown that the sequencesQ n 9f] (n=1, 2, ...) are monotone. Especially we will prove monotony in Filippi's quadrature rule and with an additional assumption onf monotony in the Clenshaw-Curtis quadrature rule.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01407873
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