Results 91 to 100 of about 1,345 (195)

Diagonal recurrence relations for the Stirling numbers of the first kind

, 2016
In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second ...
Qi, Feng
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A probabilistic generalization of the Stirling numbers of the second kind [PDF]

, 2018
Associated to each random variable Y satisfying appropriate moment conditions, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers are provided.
Lekuona, A., Adell, J.A.
core   +1 more source

Exploring probabilistic Bernstein polynomials: identities and applications

Applied Mathematics in Science and Engineering
In this paper, we introduce the probabilistic Bernstein polynomials and derive new and interesting correlations among several special functions and special number sequences such as Euler polynomials, Bernoulli polynomials of higher order, Frobenius–Euler
Ayse Karagenc, Mehmet Acikgoz, Serkan Araci   +2 more
doaj   +1 more source

Stirling numbers interpolation using permutations with forbidden subsequences

, 2002
We present a family of number sequences which interpolates between the sequences Bn, of Bell numbers, and n!. It is defined in terms of permutations with forbidden patterns or subsequences.
Leroux, P., Pergola, E., Labelle, G., Pinzani, R.   +3 more
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Probabilistic heterogeneous Stirling numbers and Bell polynomials

Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures unify several classical and probabilistic families, including those of Stirling, Lah, Bell and Lah-Bell.
Kim, Taekyun, Kim, Dae San
openaire   +2 more sources

Some Identities of the probabilistic higher order frobenius-euler polynomials and their applications

Mathematical and Computer Modelling of Dynamical Systems
Recently, there has been significant research on the generalization of various numbers using probabilistic methods. In this paper, we introduce the probabilistic higher order Frobenius-Euler polynomials which are a generalization of Frobenius-Euler ...
Jin-Woo Park, Sangbeom Park, Sang Jo Yun, Jongkyum Kwon   +3 more
doaj   +1 more source

The ordered Bell numbers as weighted sums of odd or even Stirling numbers of the second kind

, 2021
For the Stirling numbers of the second kind $S(n,k)$ and the ordered Bell numbers $B(n)$, we prove the identity $\sum_{k=1}^{n/2} S(n,2k)(2k-1)! = B(n-1)$. An analogous identity holds for the sum over odd $k$'s.
openaire   +2 more sources

A new family of q-Bernstein polynomials: probabilistic viewpoint

Arab Journal of Basic and Applied Sciences
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming [Formula: see text] is a random variable satisfying moment conditions, we use the generating function of ...
Ayse Karagenc, Mehmet Acikgoz, Serkan Araci   +2 more
doaj   +1 more source

Generating restricted classes of involutions, Bell and Stirling permutations

, 2010
We present a recursive generating algorithm for unrestricted permutations which is based on both the decomposition of a permutation as a product of transpositions and that as a union of disjoint cycles.
Poneti, Maddalena, Vajnovszki, Vincent
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Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions ^†

Mathematics
This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and ...
Feng Qi
doaj   +1 more source