Results 21 to 30 of about 10,624 (292)
q-Bernoulli Numbers Associated with q-Stirling Numbers [PDF]
Advances in Difference Equations, 2008 We consider Carlitz q-Bernoulli numbers and q-Stirling numbers of the first and the second kinds. From the properties of q-Stirling numbers, we derive many interesting formulas associated with Carlitz q-Bernoulli numbers. Finally, we will prove βn,q=â
Taekyun Kim
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Convolution Identities of Stirling Numbers
Utilitas MathematicaBy means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial identities (Theorems 3.1 and 3.3) are established as applications, that contain some well–known convolution formulae on ...
Li, Nadia N., Chu, Wenchang
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Arithmetic Identities Involving Genocchi and Stirling Numbers [PDF]
Discrete Dynamics in Nature and Society, 2009 An explicit formula, the generalized Genocchi numbers, was established and some identities and congruences involving the Genocchi numbers, the Bernoulli numbers, and the Stirling numbers were obtained.
Guodong Liu
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On Stirling numbers and Euler sums
Journal of Computational and Applied Mathematics, 1997 In this paper, we propose another yet generalization of Stirling numbers of the first kind for noninteger values of their arguments. We discuss the analytic representations of Stirling numbers through harmonic numbers, the generalized hypergeometric function and the logarithmic beta integral.
Victor S. Adamchik (5409170) +2 more
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Generalized Stirling and Lah numbers
Discrete Mathematics, 1996 The author develops three generalizations of Stirling numbers of the second kind, \(S(n,k)\), and of Lah numbers, within the theory of modular binomial lattices [\textit{P. Doubilet}, \textit{G.-C. Rota} and \textit{R. Stanley}, Proc. 6th Berkeley Sympos. Math. Statist. Probab., Univ. Calif.
Wagner, Carl G.
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A note on degenerate r-Stirling numbers
Journal of Inequalities and Applications, 2020 The aim of this paper is to study the unsigned degenerate r-Stirling numbers of the first kind as degenerate versions of the r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind as those of the r-Stirling numbers ...
Taekyun Kim +3 more
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Multi-Lah numbers and multi-Stirling numbers of the first kind
Advances in Difference Equations, 2021 In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm.
Dae San Kim +4 more
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A Note on Multi-Euler–Genocchi and Degenerate Multi-Euler–Genocchi Polynomials
Journal of Mathematics, 2023 Recently, the generalized Euler–Genocchi and generalized degenerate Euler–Genocchi polynomials are introduced. The aim of this note is to study the multi-Euler–Genocchi and degenerate multi-Euler–Genocchi polynomials which are defined by means of the ...
Taekyun Kim +3 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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Stirling Numbers of Forests and Cycles [PDF]
The Electronic Journal of Combinatorics, 2013 For a graph $G$ and a positive integer $k$, the graphical Stirling number $S(G,k)$ is the number of partitions of the vertex set of $G$ into $k$ non-empty independent sets. Equivalently it is the number of proper colorings of $G$ that use exactly $k$ colors, with two colorings identified if they differ only on the names of the colors.
David J. Galvin, Do Trong Thanh
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