Results 71 to 80 of about 706 (88)

Asymptotic analysis of the Bell polynomials by the ray method [PDF]

arXiv, 2007
We analyze the Bell polynomials $B_{n}(x)$ asymptotically as $n\to\infty$. We obtain asymptotic approximations from the differential-difference equation which they satisfy, using a discrete version of the ray method. We give some examples showing the accuracy of our formulas.
arxiv  

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

arXiv, 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.
arxiv  

Wilf conjecture [PDF]

arXiv, 2008
Let S(n,k) be the Stirling number of the second kind. Wilf conjectured that the alternating sum of S(n,k) for k from 0 to n is not zero for all n>2. In this paper, we prove that Wilf conjecture is true except at most one number with the properties of weighted Motzkin number.
arxiv  

Falling Factorials, Generating Functions, and Conjoint Ranking Tables [PDF]

Journal of Integer Sequences, 12 (2009), Article 09.7.8, 2008
We investigate the coefficients generated by expressing the falling factorial $(xy)_k$ as a linear combination of falling factorial products $(x)_l (y)_m$ for $l,m =1,...,k$. Algebraic and combinatoric properties of these coefficients are discussed, including recurrence relations, closed-form formulae, relations with Stirling numbers, and a ...
arxiv  

Investigating Exponential and Geometric Polynomials with Euler-Seidel Algorithm [PDF]

arXiv, 2009
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
arxiv  

Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series I [PDF]

arXiv, 2009
In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations are useful to obtain closed forms of some series related to harmonic numbers.
arxiv  

Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series II [PDF]

arXiv, 2010
In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series related to harmonic numbers.
arxiv  

New formulas involving Bernoulli and Stirling numbers of both kinds [PDF]

arXiv
This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.
arxiv  

A note on some identities of derangement polynomials. [PDF]

J Inequal Appl, 2018
Kim T, Kim DS, Jang GW, Kwon J.
europepmc   +1 more source

Degenerate Cauchy numbers of the third kind. [PDF]

J Inequal Appl, 2018
Pyo SS, Kim T, Rim SH.
europepmc   +1 more source