Results 31 to 40 of about 51,714 (196)
Petersen-Varchenko’s Identity for Stirling Numbers of the First Kind
Journal of the Institute of Engineering, 2018 Stirling numbers of the first kind has some interesting interpretations. In this short paper, we exhibit an elementary deduction of an identity for Sn(m) obtained by Petersen-Varchenko.
C. G. León-Vega +2 more
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A diagonal recurrence relation for the Stirling numbers of the first kind
Applicable Analysis and Discrete Mathematics, 2017 In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for ...
Feng Qi, Bai‐Ni Guo
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A Set of Conjectured Identities for Stirling Numbers of the First Kind
, 2018 3 ...
Paul Federbush
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On p-adic properties of the Stirling numbers of the first kind
Journal of Number Theory, 2015 Abstract The goal of this paper is to describe s ( n , k ) mod p e and calculate ν p ( s ( n , k ) ) for a prime p, fixed integer k ≥ 1 , and large enough e and n. Some special cases of the form s ( a p n , k ) mod p e and its relation to s ( a p n ...
T. Lengyel
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Note on the Stieltjes constants: series with Stirling numbers of the first kind
, 2016 The Stieltjes constants $ _k(a)$ appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function $ (s,a)$ about $s=1$. We generalize the integral and Stirling number series results of [4] for $ _k(a=1)$. Along the way, we point out another recent asymptotic development for $ _k(a)$ which provides convenient and ...
Mark W. Coffey
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The 2-adic valuations of Stirling numbers of the first kind
, 2018 Let $n$ and $k$ be positive integers. We denote by $v_2(n)$ the 2-adic valuation of $n$. The Stirling numbers of the first kind, denoted by $s(n,k)$, counts the number of permutations of $n$ elements with $k$ disjoint cycles. In recent years, Lengyel, Komatsu and Young, Leonetti and Sanna, and Adelberg made some progress on the $p$-adic valuations of ...
Min Qiu, Yulu Feng, Shaofang Hong
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Some identities involving degenerate Stirling numbers arising from normal ordering
AIMS Mathematics, 2022 In this paper, we derive some identities and recurrence relations for the degenerate Stirling numbers of the first kind and of the second kind, which are degenerate versions of the ordinary Stirling numbers of the first kind and of the second kind.
Taekyun Kim, Dae San Kim , Hye Kyung Kim
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New approach to λ-Stirling numbers
AIMS Mathematics, 2023 The aim of this paper is to study the $ \lambda $-Stirling numbers of both kinds, which are $ \lambda $-analogues of Stirling numbers of both kinds. These numbers have nice combinatorial interpretations when $ \lambda $ are positive integers.
Dae San Kim +2 more
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Degenerate r-truncated Stirling numbers
AIMS Mathematics, 2023 For any positive integer $ r $, the $ r $-truncated (or $ r $-associated) Stirling number of the second kind $ S_{2}^{(r)}(n, k) $ enumerates the number of partitions of the set $ \{1, 2, 3, \dots, n\} $ into $ k $ non-empty disjoint subsets, such that ...
Taekyun Kim, Dae San Kim, Jin-Woo Park
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Axioms, 2022 In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling ...
José L. Cereceda
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