A new approach for computing the inverse of confluent Vandermonde matrices via Taylor's expansion

In this paper, a novel method is presented to compute an explicit formula for the inverse of the confluent Vandermonde matrices. The proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences, notably on the situations where the Vandermonde matrices have acquired much usefulness. The method presented here is direct and straightforward, it gives explicit and compact formulas. Several examples are presented to highlight the results. The main tools are some elementary basic linear algebra.