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On weight functions which admit explicit Gauss-Turán quadrature formulas
Author(s):
Laura
Gori;
Charles
A.
Micchelli.
Journal:
Math. Comp.
65
(1996),
1567-1581.
MSC (1991):
Primary 65D32;
Secondary 41A55
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Abstract:
The main purpose of this paper is the construction of explicit Gauss-Turán quadrature formulas: they are relative to some classes of weight functions, which have the peculiarity that the corresponding  -orthogonal polynomials, of the same degree, are independent of  . These weights too are introduced and discussed here. Moreover, highest-precision quadratures for evaluating Fourier-Chebyshev coefficients are given.
References:
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Additional Information:
Laura
Gori
Affiliation:
Dipartimento di Metodi e Modelli Matematici, per le Scienze Applicate, Università ``La Sapienza", Via Antonio Scarpa , 16-00161 Roma, Italia
Charles
A.
Micchelli
Affiliation:
Mathematical Sciences Department, IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598
DOI:
10.1090/S0025-5718-96-00769-7
PII:
S 0025-5718(96)00769-7
Keywords:
Quadrature,
Tur\'{a}n-type integration rules,
generalized Jacobi weights
Received by editor(s):
November 29, 1994
Received by editor(s) in revised form:
August 9, 1995
Additional Notes:
The second author was partially supported by the Alexander von Humboldt Foundation.
The first author was supported by Ministero Università e Ricerca Scientifica e Tecnologica -- Italia.
Copyright of article:
Copyright
1996,
American Mathematical Society
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