In this paper we use Faa di Bruno's formula to associate Bell polynomial values differential equations of the form $y^{\prime}=f(y)$. That is, partial polynomials represent solution such an equation and compute special polynomials.

An extension of the Laplace transform obtained by using Laguerre-type exponentials is first shown. Furthermore, solution Blissard problem means Bell polynomials gives possibility to associate any numerical sequence a Laplace-type depending on that sequence. Computational techniques for corresponding analytic functions, involving polynomials, are derived.

Abstract In this paper, with the aid of Faà di Bruno formula and by virtue properties Bell polynomials second kind, authors define a kind notion degenerate Narumi numbers polynomials, establish explicit formulas for derive (degenerate) Cauchy numbers.

Abstract In this paper, by the Faà di Bruno formula and properties of Bell polynomials second kind, authors reconsider generating functions Hermite their squares, find an explicit for higher-order derivatives function polynomials, derive formulas recurrence relations squares.

In a previous paper we investigated the (exponential) bipartitional polynomials involving polynomial sequences of trinomial type. Our aim is to give properties of bipartitional polynomials related to the derivatives of polynomial sequences of trinomial type. Furthermore, we deduce identities involving Bell polynomials.

Abstract The notions of r -Bell polynomials and their generalization, the -Dowling are due to Mező Cheon, Jung. Recently, Nyul Rácz defined -Lah polynomials, which close relatives polynomials. In present paper, we introduce Dowling type generalization -Dowling–Lah We give a comprehensive study them using results author on -Whitney–Lah numbers, coefficients these

In the paper, by virtue of Faà di Bruno formula, with aid some properties Bell polynomials second kind, and means a general formula for derivatives ratio between two differentiable functions, authors establish explicit, determinantal, recurrent formulas generalized Eulerian polynomials.

In this paper, we consider the degenerate numbers Rn(λ) and polynomials Rn(x, λ) related to the Stirling numbers and the Bell polynomials. We also obtain some explicit formulas for degenerate numbers Rn(λ) and polynomials Rn(x, λ). AMS subject classification: 11B68, 11S40, 11S80.

Abstract The aim of this paper is to study the complete and incomplete degenerate Bell polynomials, which are versions derive some properties identities for those polynomials. In particular, we introduce new polynomials associated with fact, they coefficients reciprocal power series given by 1 plus one appearing as exponent generating function