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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Chebyshev quadrature rules for a new class of weight functions

Authors: Paul F. Byrd and Lawrence Stalla
Journal: Math. Comp. 42 (1984), 173-181
MSC: Primary 65D32
MathSciNet review: 725992
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Abstract: Proof is given that the weight functions $ w(x,p) = 1/[\pi (p + x)\sqrt {x(1 - x)} ]$ on (0, 1) admit Chebyshev quadratures for any fixed $ p \geqslant 1$, and every N. For the particular cases when $ p = 1$ and $ p = 2$, the nodes are tabulated to ten decimal places for N-point rules with $ N = 2,4,6,8$, and 12. Numerical tables are also given for a coefficient in the expression of the error term.

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Keywords: Quadrature rules
Article copyright: © Copyright 1984 American Mathematical Society