Results 51 to 60 of about 706 (88)

Some inversion formulas and formulas for Stirling numbers [PDF]

arXiv, 2010
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
arxiv  

On Relations Between the Stirling Numbers of First and Second Kind [PDF]

arXiv, 2019
Four new relations have been found between the Stirling numbers of first and second kind. They are derived directly from recently published relations.
arxiv  

A closed form for the generalized Bernoulli polynomials via Faà di Bruno's formula [PDF]

arXiv, 2020
We derive a closed form for the generalized Bernoulli polynomial of order $n$ in terms of Bell polynomials and Stirling numbers of the second kind using the Fa\`a di Bruno's formula.
arxiv  

Probabilistic degenerate Bernoulli and degenerate Euler polynomials

Mathematical and Computer Modelling of Dynamical Systems
Recently, many authors have studied degenerate Bernoulli and degenerate Euler polynomials. Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin.
Lingling Luo, Taekyun Kim, Dae San Kim, Yuankui Ma   +3 more
doaj   +1 more source

The Equivalence of Giuga's and Agoh's Conjectures [PDF]

arXiv, 2004
In this paper we show the equivalence of the conjectures of Giuga and Agoh in a direct way which leads to a combined conjecture. This conjecture is described by a sum of fractions from which all conditions can be derived easily.
arxiv  

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

Congruences on Stirling numbers and Eulerian numbers [PDF]

arXiv, 2006
In this paper, we establish some Fleck-Weisman type and Davis-Sun type congruences for the Stirling numbers and the Eulerian numbers.
arxiv  

Power sum identities with generalized Stirling numbers [PDF]

Fibonacci Quarterly, 46/47 (2009), 326-331, 2009
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
arxiv  

On degenerate multi-poly-derangement polynomials and numbers

Applied Mathematics in Science and Engineering
The problem of counting derangements was begun in 1708 by Pierre R[Formula: see text]mond de Montmort (see [Carlitz. The number of derangements of a sequence with given specification. Fibonacci Quart. 1978;16:255–258], [Clarke and Sved.
Sang Jo Yun, Jin-Woo Park
doaj   +1 more source

Periodicity of the last digits of some combinatorial sequences [PDF]

arXiv, 2013
In 1962 O. A. Gross proved that the last digits of the Fubini numbers (or surjective numbers) have a simple periodicity property. We extend this result to a wider class of combinatorial numbers coming from restricted set partitions.
arxiv