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 | References | Similar Articles | Additional Information

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.

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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:
https://doi.org/10.1090/S0025-5718-96-00769-7

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.

Article copyright:
© Copyright 1996
American Mathematical Society