Multivariate interpolation using Carlitz's inversion formulas
Multivariate rational exponential Lagrange interpolation formulas, Hermite interpolation formulas, and Hermite-Fejer interpolation formulas of the Newton type are established by using Carlitz's inversion formulas. The recurrence relation for constructing Lagrange interpolation is also given. In addition, by setting q --> 1 in the obtained formulas, we obtain the corresponding polynomial interpolation formulas with combinatorial form.
carlitz's inversion formulas lagrange interpolation hermite interpolation hermite-fejer interpolation