In this work, new closed-form formulas for the matrix exponential are provided using certain polynomials which areconstructed with the help of a generalization of Hermite's interpolation formula. Our method is direct and elementary, it gives tractable and manageable formulas not current inthe extensive literature on this essential subject. Moreover, others are recuperated and generalized. Several particular cases and examples are formulated to illustrate the method presented in this paper.
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Mouçouf et al. (2022) studied this question.