Abstract
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.
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