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
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Asymptotic expansions for the stirling numbers of the first kind
Journal of Combinatorial Theory, Series A, 1995 Let \(s(n, m)\) denote the unsigned Stirling numbers of the first kind. For any \(\eta> 0\) and natural number \(v\), the following asymptotic formula holds uniformly \[ {s(n, m)\over n!}= {1\over n} \sum_{0\leq k\leq v} {\Pi_{m,k} (\log n)\over n^k}+ O \Biggl({(\log n)^m\over m!n^{v+ 2}}\Biggr) \] for \(1\leq m\leq \eta\log n\), where \(\Pi_{m, k}(x)\)
Hsien‐Kuei Hwang
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Explicit upper bounds for the Stirling numbers of the first kind
Journal of Combinatorial Theory, Series A, 2022 José A. Adell
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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
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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
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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
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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.
Beih S. El-Desouky +3 more
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Tables of the Generalized Stirling Numbers of the First Kind [PDF]
Journal of the ACM, 1964 The generalized Stirling numbers of the first kind are defined, certain of their basic properties are discussed, and tables are given for the square grid k = 0(1)10 and j = 0(1)10 with l = -10(1)10.
William F. Pickard
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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
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A note on degenerate Stirling numbers of the first kind
, 2018 12 ...
Taekyun Kim, Dae San Kim
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