Generalized (0, m1, m2, … , ml) interpolation and extrapolation based on splines

In this article, we introduce some explicit formulas for the generalized case of (0, m1, m2, … , ml) Birkhoff interpolation and extrapolation via splines, where the elements of {mi}i=1l are not limited to the successive and finite natural numbers. Error analysis is presented and an example is given to illuminate the details and efficiency of the procedure. As a special case the existing research works for the nominal and limited values of {mi}i=1l can be obtained.