Results 31 to 40 of about 3,168 (184)
On Relations Between the Stirling Numbers of First and Second Kind
, 2019 Four new relations have been found between the Stirling numbers of first and second kind. They are derived directly from recently published relations.
Henrik Stenlund
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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 asymptotic behavior of the stirling numbers of the first kind
Journal of Combinatorial Theory, Series A, 1993 Herbert S. Wilf
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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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Euler–Riemann Zeta Function and Chebyshev–Stirling Numbers of the First Kind [PDF]
Mediterranean Journal of Mathematics, 2018 Cristina Ballantine, Mircea Merca
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