Mixed interpolation methods with arbitrary nodes (Q1298611)

The interpolation with arbitrarily given nodes from the interval of the real axis by linear combinations of \(x^i\), \(i= 0,1,\dots, n-2\) and two given functions \(C(x)\) and \(S(x)\) is considered. The Newtonian and Lagrangian interpolation formulae are investigated. The recurrent formulas for constructing interpolation formulas are suggested. The interpolation error is expressed by determinants. The interest to the current work is arrived in connection with the possible application to the solution of the differential equation.