A Newton Type Rational Interpolation Formula

Mei Fu and Alain Lascoux
Center for Combinatorics and LPMC, Nankai University,
Tianjin 300071, P.R. China

Abstract

Involving two sets of indeterminate X and C, we give a Newton type rational interpolation formula:

where

Y_n(x,X)=(x-x₁)(x-x₂)...(x-x_n),

and

(x,C)_n=(1-xc₁)(1-xc₂)...(1-xc_n).

The formula contains as a special case the original Newton interpolation, as well as the recent interpolation formula of Zhi-Guo Liu:

D_qbeing defined by

We show that some bibasic identities are special cases of our formula. Moreover, some classic q-series identities follow from the new expansion formula.