SOME UMBRAL CHARACTERISTICS OF THE ACTUARIAL POLYNOMIALS

Abstract

The utility of exponential generating functions is that they are relevant for combinatorial problems involving sets and subsets. Sequences of polynomials play a fundamental role in applied mathematics, such sequences can be described using the exponential generating functions. The actuarial polynomials a(β) n (x), n = 0, 1, 2, · · · , which was suggested by Toscano, have the following exponential generating function:

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