This paper considers Lagrange interpolation in the rational system {1/
(x - a(1)), 1/(x - a(2)), ...}, which is based on the zeros of the Che
byshev polynomial for the rational system {1, 1/(x - a(1)), 1/(x - a(2
)), ...} with distinct real poles {a(k)}(k = 1)(infinity) subset of R\
[ -1, 1]. The corresponding Lebesgue constant is estimated, and is sho
wn to be asymptotically of order In n when the poles stay outside an i
nterval which contains [ - 1, 1] in its interior. Some well-known resu
lts of classical polynomial interpolation are extended. (C) 1998 Acade
mic Press.