Experiences of Irish Mentors and Mentees Engaged in a National Nursing and Midwifery Mentorship Programme: Mixed Methods Study With a Qualitative Focus on Mentors' Views. [PDF]
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A STUDY ON MULTI-STIRLING NUMBERS OF THE FIRST KIND
Fractals, 2022In 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 ...
Ma, Yuankui +4 more
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Convolution Identities for Stirling Numbers of the First Kind
Integers, 2010AbstractWe derive several new convolution identities for the Stirling numbers of the first kind. As a consequence we obtain a new linear recurrence relation which generalizes known relations.
Takashi Agoh, Karl Dilcher
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A Multitude of Expressions for the Stirling Numbers of the First Kind
Integers, 2010AbstractIt is shown that the Stirling numbers of the first kind can be expressed in the ...
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Tables of the Generalized Stirling Numbers of the First Kind
Journal of the ACM, 1964The generalized Stirling numbers of the first kind are defined, certain of their basic properties are discussed, and tables are given for the square grid k = 0(1)10 and j = 0(1)10 with l = -10(1)10.
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A Combinatorial Approach to the Stirling Numbers of the First Kind with Higher Level
Studia Scientiarum Mathematicarum Hungarica, 2021In this paper, we investigate a generalization of the classical Stirling numbers of the first kind by considering permutations over tuples with an extra condition on the minimal elements of the cycles. The main focus of this work is the analysis of combinatorial properties of these new objects.
Komatsu, Takao +3 more
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Some applications of the stirling numbers of the first and second kind
Journal of Applied Mathematics and Computing, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Masjed-Jamei, Mohammad +2 more
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The modular (r,s)-Stirling numbers of the first kind
Discrete Mathematics, Algorithms and ApplicationsWe propose a new generalization of the [Formula: see text]-Stirling numbers of the first kind and their analogs. These numbers appear as specialization of a new class of symmetric function, and they can be seen as a natural generalizations of the [Formula: see text]-Stirling numbers of the first kind and their analogs.
Bazeniar Abdelghafour, Moussa Ahmia
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The r-Stirling numbers of the first kind in terms of the Möbius function
The Ramanujan Journal, 2020For any \(r\) positive integer, the \(r\)-Stirling number of the first kind \(\binom{n}{k}_r\) is defined as the number of permutations of \(\{1,2,\dots,n\}\) with exactly \(k\) cycles, such that the numbers \(1,2,\dots,r\) are in distinct cycles. The Möbius function of the partition lattice is defined in the following way: if \(v\) is a partition of ...
Cristina Ballantine, Mircea Merca
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Asymptotics of the Chebyshev–Stirling numbers of the first kind
Integral Transforms and Special Functions, 2015ABSTRACTThe asymptotic behaviour of the Chebyshev–Stirling numbers of the second kind, a special case of the Jacobi–Stirling numbers, has been established in a recent paper by Gawronski, Littlejohn and Neuschel. In this paper, we provide an asymptotic formula for the Chebyshev–Stirling numbers of the first kind.
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