Results 11 to 20 of about 51,954 (284)
A STUDY ON MULTI-STIRLING NUMBERS OF THE FIRST KIND
Fractals, 2022 In this paper, we define the multi-Stirling numbers of the first kind by means of the multiple logarithm and as a generalization of the Stirling numbers of the first kind. Then we introduce two additional special numbers by using the multiple logarithm, namely the modified multi-Bernoulli numbers as a generalization of the higher-order Bernoulli ...
Yuankui Ma +4 more
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A Family of Generalized Stirling Numbers of the First Kind
Applied Mathematics, 2014 A modified approach via differential operator is given to derive a new family of generalized Stirling numbers of the first kind. This approach gives us an extension of the techniques given by El-Desouky [1] and Gould [2]. Some new combinatorial identities and many relations between different types of Stirling numbers are found.
B. S. El-Desouky +3 more
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On the $p$-adic properties of Stirling numbers of the first kind [PDF]
Acta Mathematica Hungarica, 2019 Let $n, k$ and $a$ be positive integers. The Stirling numbers of the first kind, denoted by $s(n,k)$, count the number of permutations of $n$ elements with $k$ disjoint cycles. Let $p$ be a prime. In recent years, Lengyel, Komatsu and Young, Leonetti and Sanna, Adelberg, Hong and Qiu made some progress in the study of the $p$-adic valuations of $s(n,k)$
Shaofang Hong, Min Qiu
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Some identities on λ-analogues of r-Stirling numbers of the first kind
, 2020 12
Taekyun Kim, Dae San Kim
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On r-Stirling Type Numbers of the First Kind
Turkish Journal of Analysis and Number Theory, 2019 Some combinatorial properties of -Stirling numbers are proved. Moreover, two asymptotic formulas for -Stirling numbers of the first kind derived using different methods are discussed and corresponding asymptotic formulas for the -Stirling type numbers of the first kind are obtained as corollaries.
Cristina B. Corcino, Roberto B. Corcino
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A note on degenerate Stirling numbers of the first kind [PDF]
, 2018 12 ...
Taekyun Kim, Dae San Kim
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On Non-central Stirling Numbers of the First Kind [PDF]
, 2009 It is shown in this note that non-central Stirling numbers s(n,k,a) of the first kind naturally appear in the expansion of derivatives of the product of a power function and a logarithn function. We first obtain a recurrence relation for these numbers, and then, using Leibnitz rule we obtain an explicit formula for these numbers.
Milan Janjić
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A diagonal recurrence formula for Stirling numbers of the first kind [PDF]
, 2013 In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.Comment: 7 ...
Feng Qi
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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.
José A. Adell
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The Extended Legendre-Stirling Numbers of the First Kind
DEStech Transactions on Engineering and Technology Research, 2016 The Legendre-Stirling numbers of the first kind j n Ps are defined by the coefficients of Taylor expansion of the function x(x 2)(x 6)(x (n 1)n) by Andrews and Littlejohn (see "A combinatorial interpretation of the Legendre-Stirling numbers", Proc. Amer. Math. Soc, 137: 2581-2590, 2009). In this paper, two new kinds of numbers jn Ps (n
Fangqing Wen +4 more
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