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On weight functions which admit explicit Gauss-Turán quadrature formulas

Authors: Laura Gori and Charles A. Micchelli
Journal: Math. Comp. 65 (1996), 1567-1581
MSC (1991): Primary 65D32; Secondary 41A55
MathSciNet review: 1361808
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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 $s$-orthogonal polynomials, of the same degree, are independent of $s$. These weights too are introduced and discussed here. Moreover, highest-precision quadratures for evaluating Fourier-Chebyshev coefficients are given.

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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

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.
Article copyright: © Copyright 1996 American Mathematical Society