Об асимптотических разложениях для чисел Стирлинга первого и второго рода@@@On asymptotic expansions of Stirling numbers of the first and second kinds
Александр Николаевич Тимашeв,Aleksandr Nikolaevich Timashev +1 more
- Vol. 10, Iss: 3, pp 148-159
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The article was published on 1998-01-01 and is currently open access. It has received 7 citations till now. The article focuses on the topics: Stirling number.read more
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Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach
TL;DR: Using the saddle point method and Cauchy's integral formula, asymptotic results in central and non-central regions are obtained and the celebrated Goncharov theorem is revisited with more precision.
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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.
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On the distribution of the number of cycles of a given length in the class of permutations with known number of cycles
TL;DR: In this paper, the authors considered the set of permutations of degree n with W cycles and obtained the asymptotic values of the mathematical expectation and the variance of this random variable and proved the limit theorems on the convergence to the Poisson and the Gaussian distributions as Λ, Ν -»· oo.
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On asymptotic expansions in local limit theorems for equiprobable schemes of allocating particles to distinguishable cells
TL;DR: In this article, Kolchin et al. considered equiprobable schemes of allocating indistinguishable and distinguishable particles to distinguishable cells, and obtained asymptotic expansions in local theorems on large deviations.