The Coefficients of the Polynomial Interpolation in Terms of Finite Differences and Numerical Differentiations

In this note, the polynomial interpolation of degree n passing through n+1 distinct points is considered. The coefficients of the polynomial interpolation are investigated in terms of finite differences and numerical differentiations. The coefficients are formulated by the use of divided differences and correlated with forward, backward differences and numerical differentiations. It is seen that the coefficients of the polynomial interpolation can be found and computed by using finite differences, numerical differentiations and generating special formulae for equidistant points or not.