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Representations of Stirling Numbers of the First Kind by Multiple Integrals
Integers, 2015 See the abstract in the attached pdf.
Takashi Agoh, Karl Dilcher
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A Note on Some Identities of New Type Degenerate Bell Polynomials
Mathematics, 2019 Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced.
Taekyun Kim +3 more
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Refinements of the Bell and Stirling numbers [PDF]
Transactions on Combinatorics, 2018 We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial ...
Tanay Wakhare
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Closed Form Expressions for the Stirling Numbers of the First Kind
Integers, 2017 See the abstract in the attached pdf.
José A. Adell, Alberto Lekuona
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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 \(\Pi_{m, k}(x)\)
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A Symmetric Sum Involving the Stirling Numbers of the First Kind
European Journal of Combinatorics, 1984 Let \(\{a_i\}^n_{i=1}\) be a sequence of natural numbers, \(0\leq a_i\leq n\) for \(i=1,\dots,n\), and \(A_{nm}\) be an \(n\times m\) array associated with this sequence, whose entries \(\alpha_{ij}=0,1\) such that \(\sum_{j=1}^m \alpha_{ij}=a_i\), \(i=1,\dots,n\), \(j=1,\dots,m\).
A. M. Khidr, B. S. El-Desouky
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Explicit upper bounds for the Stirling numbers of the first kind
Journal of Combinatorial Theory, Series A, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The asymptotic behavior of the stirling numbers of the first kind
Journal of Combinatorial Theory, Series A, 1993 The asymptotic expansion for the Stirling number of the first kind \({n \brack k}\) for fixed \(k\) together with examples has been obtained.
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Sum rules for permutations with fixed points involving Stirling numbers of the first kind
Indonesian Journal of CombinatoricsWe propose sum rules for permutations pn(k) of the ensemble {1,2,...,n} with k fixed points, in the form of partial sums of their moments. The corresponding identities involve Stirling numbers of the first kind s(q,r).
Jean-Christophe Pain
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Advanced Materials Technologies, EarlyView.A label‐free impedimetric biosensor based on electroactive 3D porous graphene foam enables ultrasensitive and selective detection of CD81 protein and MCF‐7 cell‐derived extracellular vesicles in human serum. Detection limits of 0.048 fg/mL for CD81 and ∼24 EVs/mL are achieved, demonstrating a robust platform for selective, label‐free, and ...
Michael Robert Furness +11 more
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