Weight functions for Chebyshev quadrature

Abstract

In this paper, we investigate if the weight function ( 1 − x 2 ) − 1 / 2 R ( x ) {(1 - {x^2})^{ - 1/2}}R(x) , where R ( x ) R(x) is a rational function of order (1,1), admits Chebyshev quadratures. Many positive examples are provided. In particular, we have proved that the answer is affirmative if R ( x ) = 1 + b x R(x) = 1 + bx , | b | > 0.27846 … |b| > 0.27846 \ldots .