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In this paper, we use particular polynomials to establish some results on the real rootedness of polynomials. The considered polynomials are Bell polynomials and Hermite polynomials.

The aim of this work is to establish some properties of the coefficients of the chromatic polynomials of special graphs. An application on (restricted) Stirling numbers of the second kind is considered. [ABSTRACT FROM AUTHOR]

In this paper, we define a sequence of polynomials P n ( α ) ( x | A , H ) depending only on the choice of two analytic functions A and H in a neighborhood of zero. For a pair of compositional inverses A and B , we will show the identity P n ( α ) ( x | B , H ∘ B ) = P n ( n + 1 − α ) ( 1 − x | A , A ′ H ) , which generalize the Carlitz's identity on Bernoulli polynomials. [ABSTRACT FROM AUTHOR]

The main object of this paper is to give an application of the r -Whitney numbers to the values at rational arguments of the high-order Bernoulli and Euler polynomials. The obtained formulas generalize the known formulas of the Bernoulli numbers of both kinds. [ABSTRACT FROM AUTHOR]