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Asymptotic estimates of Stirling numbers
Nico M. Temme
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The article was published on 1992-01-01 and is currently open access. It has received 85 citations till now. The article focuses on the topics: Stirling number & Asymptotic analysis.read more
Citations
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Book ChapterDOI
Interpolation function of generalized q −bernstein-type basis polynomials and applications
TL;DR: A new generating function is constructed for the generalized q -Bernstein-type basis polynomials and fundamental properties of these polynOMials are derived by applying Mellin transform.
Journal ArticleDOI
New properties of r -Stirling series
TL;DR: The summation of series involving the Stirling numbers of the first kind can be found in several works but there is no such a computation for the second kind let alone the r-Stirlings as mentioned in this paper.
Journal ArticleDOI
Asymptotics of Stirling and Chebyshev-Stirling Numbers of the Second Kind
TL;DR: In this paper, asymptotic analysis of the Chebyshev-Stirling numbers with uniformity properties and the leading terms are given explicitly and they contain elementary expressions are established.
Journal ArticleDOI
A Poisson * Geometric Convolution Law for the Number of Components in Unlabelled Combinatorial Structures
TL;DR: In this paper, the authors derived precise asymptotic estimates for N(n, m), as n→∞ and m varies through all possible values (in general 1≤m≤n).
Journal ArticleDOI
On the number of siblings and p-th cousins in a large population sample
TL;DR: The results show that a substantial fraction of individuals in the sample will have at least a second cousin if the sampling fraction (K / N) is on the order of $$10^{-2}$$10-2, which confirms that, for large cohort samples, relatedness among individuals cannot easily be ignored.
References
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Book
Asymptotic enumeration methods
TL;DR: In this article, the saddle point and large singularities of analytic functions are used for graphical enumeration, including implicit functions, recurrences, and combinations of methods, which are related to our work.
Journal ArticleDOI
A Unified Approach to Generalized Stirling Numbers
Leetsch C. Hsu,Peter J. S. Shiue +1 more
TL;DR: In this article, it was shown that various well-known generalizations of Stirling numbers of the first and second kinds can be unified by starting with transformations between generalized factorials involving three arbitrary parameters.
Journal ArticleDOI
Probabilistic Bounds on the Coefficients of Polynomials with Only Real Zeros
TL;DR: Alignments and approximations for finite sequences, called Polya frequency sequences, which follow from their probabilistic representation are reviewed, finding a number of improvements of known estimates.
Journal ArticleDOI
A General Upper Bound for the Satisfiability Threshold of Randomr-SAT Formulae
O Dubois,Y Boufkhad +1 more
TL;DR: A general upper bound of the threshold forr-SAT formulae is established giving a value for 3-S AT of 4.64, significantly improving the previous best upper bound.
Book ChapterDOI
Tighter Bounds for the Determinisation of Büchi Automata
TL;DR: This paper proposes a determinisation technique that is simpler than the constructions of Safra, Piterman, and Muller and Schupp, because it separates the principle acceptance mechanism from the concrete acceptance condition.