Explicit upper bounds for the Stirling numbers of the first kind
Journal of Combinatorial Theory, Series A, 2022 José A. Adell
semanticscholar +5 more sources
Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind [PDF]
Filomat, 2014 In the paper, by establishing a new and explicit formula for computing the n-th derivative of the reciprocal of the logarithmic function, the author presents new and explicit formulas for calculating Bernoulli numbers of the second kind and Stirling numbers of the first kind.
Feng Qi
semanticscholar +6 more sources
Petersen-Varchenko’s Identity for Stirling Numbers of the First Kind
Journal of the Institute of Engineering, 2018 Stirling numbers of the first kind has some interesting interpretations. In this short paper, we exhibit an elementary deduction of an identity for Sn(m) obtained by Petersen-Varchenko.
C. G. León-Vega +2 more
semanticscholar +5 more sources
A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind [PDF]
Publications de l'Institut Mathematique, 2015 We find an explicit formula for computing the Bernoulli numbers of the second kind in terms of the signed Stirling numbers of the first kind.
Feng Qi
semanticscholar +6 more sources
Integral representations and properties of Stirling numbers of the first kind
Journal of Number Theory, 2013 Abstract In the paper, the author establishes several integral representations and properties of Stirling numbers of the first kind.
Feng Qi
semanticscholar +4 more sources
A distribution function from population genetics statistics using Stirling numbers of the first kind: Asymptotics, inversion and numerical evaluation [PDF]
Mathematics of Computation, 2021 Stirling numbers of the first kind are common in number theory and combinatorics; through Ewen's sampling formula, these numbers enter into the calculation of several population genetics statistics, such as Fu's Fs.
Swaine L. Chen, Nico Μ. Τemme
semanticscholar +5 more sources
Exact p-adic valuations of Stirling numbers of the first kind
Journal of Number Theory, 2017 Abstract For any positive integer k and prime p, we define an explicit set A k , p of positive integers n, having positive upper and lower density, on which the p-adic valuation of the Stirling number of the first kind s ( n + 1 , k + 1 ) is a nondecreasing function of n and is given exactly by a simple formula.
Takao Komatsu, Paul Thomas Young
semanticscholar +4 more sources
Asymptotic expansions for the stirling numbers of the first kind
Journal of Combinatorial Theory, Series A, 1995 Hsien‐Kuei Hwang
semanticscholar +4 more sources
A Family of Generalized Stirling Numbers of the First Kind [PDF]
Applied Mathematics, 2014 A modified approach via differential operator is given to derive a new family of generalized Stirling numbers of the first kind. This approach gives us an extension of the techniques given by El-Desouky [1] and Gould [2]. Some new combinatorial identities and many relations between different types of Stirling numbers are found.
B. S. El-Desouky +3 more
openalex +3 more sources
A STUDY ON MULTI-STIRLING NUMBERS OF THE FIRST KIND
Fractals, 2022 In this paper, we define the multi-Stirling numbers of the first kind by means of the multiple logarithm and as a generalization of the Stirling numbers of the first kind.
Yuankui Ma +4 more
openalex +2 more sources