Results 51 to 60 of about 1,536,850 (314)
Discrete Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrews, G.E. +2 more
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A Note on Some Identities of New Type Degenerate Bell Polynomials
Mathematics, 2019 Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced.
Taekyun Kim +3 more
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Congruences for the Stirling numbers and associated Stirling numbers [PDF]
Acta Arithmetica, 1990 Let s(n,k) and S(n,k) be the Stirling numbers of the first and second kind, respectively. The author proves that if \(k+n\) is odd, then \[ s(n,k)\equiv 0 (mod\left( \begin{matrix} n\\ 2\end{matrix} \right)),\quad S(n,k)\equiv 0 (mod\left( \begin{matrix} k+1\\ 2\end{matrix} \right)).
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On the asymptotic normality of the Legendre-Stirling numbers of the second kind
, 2014 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,
Gawronski, Wolfgang +2 more
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Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers
, 1992 The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a set of ...
Abramowitz M +17 more
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Probabilistic Stirling numbers and applications
Aequationes MathematicaeWe introduce probabilistic Stirling numbers of the first kind sY(n,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
J. A. Adell, Beáta Bényi
semanticscholar +1 more source
Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Scurr, Raymond, Olive, Gloria
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Advanced Intelligent Systems, EarlyView.Natural fliers achieve remarkable aerial performance through diverse wing neuromechanical systems integrating actuation, sensing, and control. This study synthesizes neuromechanical architectures in insects and hummingbirds, identifying two key functional types‐Dual Neural‐Mechanical Oscillator and Neurally‐modulated Mechanical Oscillator‐ and ...
Suyash Agrawal +4 more
wiley +1 more source
On q-Euler Numbers Related to the Modified q-Bernstein Polynomials
Abstract and Applied Analysis, 2010 We consider q-Euler numbers, polynomials, and q-Stirling numbers of first and second kinds. Finally, we investigate some interesting properties of the modified
Min-Soo Kim, Daeyeoul Kim, Taekyun Kim
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Study on Degenerate Stirling Numbers
European Journal of Pure and Applied MathematicsIn this paper, we consider various Stirling numbers of both kinds, including the unsigned degenerate Stirling numbers of the first kind, the degenerate Stirling numbers of the second kind, the unsigned degenerate r-Stirling numbers of the first kind and ...
Dae San Kim, Taekyun Kim, J. Kwon
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