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In the paper, the authors discuss the Bell polynomials and a sequence of polynomials applied to the theory of differential equations. Concretely speaking, the authors find four explicit formulas for these polynomials and for derivatives of generating functions of these polynomials, establish four identities between these two kinds of polynomials, and significantly simplify some known results.
The main propose of this article is to investigate and modify Hermite type polynomials, Milne-Thomson type polynomials and Poisson–Charlier type polynomials by using generating functions and their functional equations. By using functional equations of the generating functions for these polynomials, we not only derive some identities and relations including the Bernoulli numbers and polynomials, the...
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