Results 11 to 20 of about 50,310 (297)
On the asymptotic normality of the Legendre–Stirling numbers of the second kind
European Journal of Combinatorics, 2015 For the Legendre-Stirling numbers of the second kind asymptotic formulae are derived in terms of a local central limit theorem. Thereby, supplements of the recently published asymptotic analysis of the Chebyshev-Stirling numbers are established. Moreover, we provide results on the asymptotic normality and unimodality for modified Legendre-Stirling ...
Wolfgang Gawronski +2 more
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Some identities related to degenerate Stirling numbers of the second kind
Demonstratio Mathematica, 2022 The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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An explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind [PDF]
, 2014 In the paper, the author finds an explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind.
Feng Qi (祁锋)
semanticscholar +4 more sources
On stirling numbers of the second kind [PDF]
Journal of Combinatorial Theory, 1969 AbstractWe first find inequalities between the Stirling numbers S(n, r) for fixed n, then introduce functions L and U such that L(n, r)≤S(n, r)≤U(n, r), and finally obtain the asymptotic value n/log n for the value of r for which S(n, r) is maximal.
A.J. Dobson, B.C. Rennie
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Some Identities Involving $q$-Stirling Numbers of the Second Kind in Type B [PDF]
Electronic Journal of Combinatorics, 2023 The recent interest in type B $q$-Stirling numbers of the second kind prompted us to give a type B analogue of a classical identity connecting the $q$-Stirling numbers of the second kind and Carlitz's major $q$-Eulerian numbers, which turns out to be a ...
Ming-Jian Ding, Jiang Zeng
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The Hadamard product of series with Stirling numbers of the second kind and other special numbers [PDF]
Electronic Journal of Mathematics, 2022 We evaluate in closed form a number of power series where the coefficients are products of Stirling numbers of the second kind and other special numbers or polynomials. The results include harmonic, hyperharmonic, derangement, Cauchy, Catalan numbers, zeta
Khristo N. Boyadzhiev, Robert Frontczak
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A probabilistic generalization of the Stirling numbers of the second kind [PDF]
Journal of Number Theory, 2018 Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers are provided.
José A. Adell, Alberto Lekuona
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Asymptotics of Stirling numbers of the second kind [PDF]
Proceedings of the American Mathematical Society, 1974 This work was partially supported by the Office of Naval Research under Contract Number NR 042-286 at the Naval Postgraduate School.
W. E. Bleick, Peter C. C. Wang
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A q, r-analogue for the Stirling numbers of the second kind of Coxeter groups of type B [PDF]
Pure Mathematics and Applications, 2022 A generalization of the Stirling numbers of the second kind of type B is given in two different directions. One generalization is via their q-analogue and the other one uses r distinguished elements.
Eli Bagno, David Garber, Takao Komatsu
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The Lucas congruence for Stirling numbers of the second kind [PDF]
Acta Arithmetica, 2000 0. Introduction. The numbers introduced by Stirling in 1730 in his Methodus differentialis [11], subsequently called “Stirling numbers” of the first and second kind, are of the greatest utility in the calculus of finite differences, in number theory, in the summation of series, in the theory of algorithms, in the calculation of the Bernstein ...
Roberto Sánchez-Peregrino
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