The formulae for computing the coefficients of the polynomial interpolation passing through n+1 distinct points

This paper deals with the polynomial interpolation of degree at most n passing through n 1 distinct points. The coefficients of the polynomial interpolation are written as a system of the linear equations. The system consisting of the coefficients is solved by the use of the closed form of the inverse of the Vandermonde matrix. The coefficients of the interpolation are obtained by using the sum and product symbols. The algorithm for the coefficients of the polynomial interpolation is developed by generating formulae. Also, these coefficients for equidistant points are formulated by forward difference. It is seen that the coefficients of the interpolation of degree at most n passing through n 1 distinct points can be computed directly by generating specialformulae and can be applied easily to the polynomial interpolation. Numerical examples are represented.Anahtar KelimelerVandermonde matrix, coefficients of the polynomial interpolation, forward difference