Results 81 to 90 of about 30,485 (178)

Combinatorial Physics, Normal Order and Model Feynman Graphs

, 2003
The general normal ordering problem for boson strings is a combinatorial problem. In this note we restrict ourselves to single-mode boson monomials.
Blasiak, P., Duchamp, G., Horzela, A., Penson, K. A., Solomon, A. I.   +4 more
core   +1 more source

Recurrences of Stirling and Lah numbers via second kind Bell polynomial

Discrete Mathematics Letters, 2020
Summary: In the paper, by virtue of several explicit formulas for special values and a recurrence of the Bell polynomials of the second kind, the authors derive several recurrences for the Stirling numbers of the first and second kinds, for 1-associate Stirling numbers of the second kind, for the Lah numbers, and for the binomial coefficients.
Qi F., Natalini P., Ricci P. E.
openaire   +3 more sources

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

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

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

Bell Numbers and Stirling Numbers of the Mycielskian of Trees

14 pages, 3 tables, 0 ...
Allagan, J., Morgan, G., Sinclair, D.
openaire   +2 more sources

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

BELL PERMUTATIONS AND STIRLING NUMBERS INTERPOLATION

, 1999
A family of number sequences which interpolates the sequences of Bell numbers and n!
PERGOLA, ELISA, PINZANI, RENZO, G. LABELLE, P. LEROUX   +3 more
openaire   +1 more source

Extended degenerate Stirling numbers of the second kind and extended degenerate Bell polynomials

, 2017
In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials associated with them.
Kim, Taekyun, Kim, Dae San
openaire   +2 more sources

Connections between Bell numbers, Stirling numbers of first and second kind and Partitions. Evaluation of these numbers.

, 2020
Bell and Stirling numbers of first and second kind tell the number of ways that n objects, or n cycles in the case of Stirling numbers of first kind, can be distributed in k cells. They are usually obtained through recurrence rules. However, recurrence rules only tell how many distributions are possible, not the specific form of each distribution, so ...
openaire   +1 more source