Properties and applications of Bell polynomials of two variables (original) (raw)

Various applications of the (exponential) complete Bell polynomials

2010

In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also show how the (exponential) complete Bell polynomials feature in a number of other areas of mathematical interest.

Multivariate Stirling polynomials of the first and second kind

Discrete Mathematics, 2015

Two doubly indexed families of homogeneous and isobaric polynomials in several indeterminates are considered: the (partial) exponential Bell polynomials B n,k and a new family S n,k ∈ Z[X 1 ,. .. ,X n−k+1 ] such that X −(2n−1)

Derivation of Bell Polynomials of the Second Kind

Arxiv preprint arXiv:1104.5065, 2011

New methods for derivation of Bell polynomials of the second kind are presented. The methods are based on an ordinary generating function and its composita. The relation between a composita and a Bell polynomial is demonstrated. Main theorems are written and examples of Bell polynomials for trigonometric functions, polynomials, radicals, and Bernoulli functions are given.

Bell-Based Bernoulli Polynomials with Applications

Axioms, 2021

In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order α and investigate multifarious correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Bell-based Bernoulli polynomials of order α. Moreover, we attain several interesting formulas of Bell-based Bernoulli polynomials of order α arising from umbral calculus.

On new identities for Bell's polynomials

Discrete Mathematics, 2005

In this work, we propose two new methods for the determination of new identities for Bell's polynomials. The first method is based on the Lagrange inversion formula, and the second is based on the binomial sequences. These methods allow the easy recovery of known identities and deduction of some new identities of these polynomials.

New identities for Bell’s polynomials New approaches

In this work we suggest a new approach to the determination of new identities for Bell's polynomials, based on the Lagrange inversion formula, and the binomial sequences. This approach allows the easy recovery of known identities and deduction of some new identities including these polynomials.

The role of binomial type sequences in determination identities for Bell polynomials

2008

Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and binomial type sequences in first part, and, we generalize the results obtained in [4] in second part.

On Generalized Bell Polynomials

It is shown that the sequence of the generalized Bell polynomials Sn(x) is convex under some restrictions of the parameters involved. A kind of recurrence relation for Sn(x) is established, and some numbers related to the generalized Bell numbers and their properties are investigated.