Lagrange Interpolation and Quadrature Formula in Rational Systems Original Research Article

This paper considers Lagrange interpolation in the rational system {1/(x−a1), 1/(x−a2), …}, which is based on the zeros of the Chebyshev polynomial for the rational system {;1, 1/(x−a1), 1/(x−a2), …} with distinct real poles {ak}∞k=1R\[−1, 1]. The corresponding Lebesgue constant is estimated, and is shown to be asymptotically of order ln nwhen the poles stay outside an interval which contains [−1, 1] in its interior. Some well-known results of classical polynomial interpolation are extended.