Chebyshev quadrature rules for a new class of weight functions

Abstract

Proof is given that the weight functions w ( x , p ) = 1 / [ π ( p + x ) x ( 1 − x ) ] w(x,p) = 1/[\pi (p + x)\sqrt {x(1 - x)} ] on (0, 1) admit Chebyshev quadratures for any fixed p ⩾ 1 p \geqslant 1 , and every N. For the particular cases when p = 1 p = 1 and p = 2 p = 2 , the nodes are tabulated to ten decimal places for N-point rules with N = 2 , 4 , 6 , 8 N = 2,4,6,8 , and 12. Numerical tables are also given for a coefficient in the expression of the error term.