Chebyshev quadrature rules for a new class of weight functions

Byrd, Paul F.; Stalla, Lawrence

doi:10.1090/S0025-5718-1984-0725992-1

Chebyshev quadrature rules for a new class of weight functions
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by Paul F. Byrd and Lawrence Stalla PDF

Math. Comp. 42 (1984), 173-181 Request permission

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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