A research on the new polynomials involved with the central factorial numbers, Stirling numbers and others polynomials
نویسندگان
چکیده
منابع مشابه
On degenerate numbers and polynomials related to the Stirling numbers and the Bell 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.
متن کاملOn Generalized Stirling Numbers and Polynomials
In this paper we prove that some results concerned the generalized Stirling numbers are the consequence of the results of Toscano and Chak. The new explicit expressions for generalized Stirling numbers are also given.
متن کاملApplications of Chromatic Polynomials Involving Stirling Numbers
The Stirling numbers of the second kind, denoted S(n, k), are the number of ways to partition n distinct objects into k nonempty subsets. We use the notation [n] = {1, 2,. . ., n} and sometimes refer to the subsets as blocks. The initial conditions are defined as: S(0, 0) = 1, S(n, 0) = 0, for n ≥ 1, and S(n, k) = 0 for k > n. We also have S(n, 2) = 2 n−1 − 1 and S(n, n − 1) = n 2. The numbers ...
متن کاملExponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals
and Applied Analysis 3 and continuing like that to S8. For large n this method is not convenient. However, later that year Ligowski 4 suggested a better method, providing a generating function for the numbers Sn: e z ∞ ∑ k 0 e k! ∞ ∑ k 0 ∞ ∑ n 0 k k! z n! ∞ ∑ n 0 Sn z n! . 2.4 Further, an effective iteration formula was found Sn n−1 ∑ j 0 ( n − 1 j ) Sj 2.5 by which every Sn can be evaluated st...
متن کاملGeneralized Stirling numbers, exponential Riordan arrays and orthogonal polynomials
We define a generalization of the Stirling numbers of the second kind, which depends on two parameters. The matrices of integers that result are exponential Riordan arrays. We explore links to orthogonal polynomials by studying the production matrices of these Riordan arrays. Generalized Bell numbers are also defined, again depending on two parameters, and we determine the Hankel transform of t...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2014
ISSN: 1029-242X
DOI: 10.1186/1029-242x-2014-26