Results 71 to 80 of about 95,348 (153)

Series involving degenerate harmonic numbers and degenerate Stirling numbers

Applied Mathematics in Science and Engineering
Recently, degenerate harmonic numbers and degenerate hyperharmonic numbers are introduced by Kim-Kim. In this paper, we study the series involving the degenerate harmonic numbers and degenerate Stirling numbers and investigate those properties.
Lingling Luo, Yuankui Ma, Taekyun Kim, Rongrong Xu   +3 more
doaj   +1 more source

On a generalization of derangement polynomials and numbers

Demonstratio Mathematica
In T. Kim, D. S. Kim, and D. V. Dolgy, Probabilistic derangement numbers and polynomials, Math. Comput. Model. Dyn. Syst. 31 (2025), no. 1, 2529188, Kim-Kim defined the probabilistic derangement polynomials and numbers and found some properties of those ...
Yun Sang Jo, Park Jin-Woo
doaj   +1 more source

Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function

Axioms, 2019
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new ...
Irem Kucukoglu, Burcin Simsek, Yilmaz Simsek   +2 more
doaj   +1 more source

The Jacobi-Stirling Numbers

, 2011
17 pages, 3 ...
Andrews, George E., Egge, Eric S., Gawronski, Wolfgang, Littlejohn, Lance L.   +3 more
openaire   +2 more sources

Generalized Bell Numbers and Peirce Matrix via Pascal Matrix

International Journal of Mathematics and Mathematical Sciences, 2018
With the Stirling matrix S and the Pascal matrix T, we show that TkS (k≥0) satisfies a type of generalized Stirling recurrence. Then, by expressing the sum of components of each row of TkS as k-Bell number, we investigate properties of k-Bell numbers as ...
Eunmi Choi
doaj   +1 more source

Combinatorial Properties and Values of High-Order Eulerian Numbers

Axioms
This paper studies higher-order Eulerian numbers based on Stirling permutations and utilizing Eulerian triangles. It primarily focuses on the chain of higher-order Eulerian numbers, higher-order Eulerian polynomials, and higher-order Eulerian fractions ...
Tian-Xiao He
doaj   +1 more source

A note on q-analogue of Hermite-poly-Bernoulli numbers and polynomials [PDF]

Mathematica Moravica, 2019
In this paper, we introduce the Hermite-based poly-Bernoulli numbers and polynomials with q-parameter and give some of their basic properties including not only addition property, but also derivative properties and integral representations.
Khan Waseem A., Khan Idrees A., Ali Musharraf   +2 more
doaj  

Stirling numbers and records

Journal of Combinatorial Theory, Series A, 1983
AbstractThe equivalence of two classical sums giving the Stirling numbers of first kind results from a joint law for records.
openaire   +2 more sources

Stirling numbers and inverse factorial series [PDF]

Contributions to Mathematics, 2023
Khristo N. Boyadzhiev
doaj   +1 more source

Generalized Stirling Numbers I

, 2018
We consider generalized Stirling numbers of the second kind $% S_{a,b,r}^{ _{s}, _{s},r_{s},p_{s}}\left( p,k\right) $, $% k=0,1,\ldots .rp+\sum_{s=2}^{L}r_{s}p_{s}$, where $a,b, _{s}, _{s} $ are complex numbers, and $r,p,r_{s},p_{s}$ are non-negative integers given, $s=2,\ldots ,L$.
openaire   +2 more sources