Results 161 to 170 of about 4,691 (197)

On the analytic extension of Stirling numbers of the first kind

Journal of Difference Equations and Applications, 2010
We present an analytic extension of the unsigned Stirling numbers of the first kind that is in a certain sense unique in its coincidence with the Stirling polynomials. We examine and compare our extension to previous extensions of (signed) Stirling numbers of the first kind given by Butzer et al. (2007, J. Difference Equ. Appl., 13) and of the unsigned
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A probabilistic approach to stirling numbers of the first kind

Communications in Statistics - Theory and Methods, 1990
Let be a sequence of independent random variables which take on one of the values 0, 1 with specified probabilities where B1=l with probability one. Then the sum takes on one of the values l,…,n with the probabilities related to Stirling numbers of the first kind. Using these random variables we show several properties of the numbers.
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$λ$-analogues of r-Stirling numbers of the first kind

2018
12
Kim, Taekyun, Kim, Dae san
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Generating functions for extended Stirling numbers of the first kind

J. Integer Seq., 2014
Summary: In this paper we extend the definition of Stirling numbers of the first kind by way of a special multiset. This results in a family of number triangles for which we show how to obtain ordinary generating functions for the rows and exponential generating functions for the columns. The latter are derived via a recursive process. We also indicate
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A probabilistic approach to expressions of Stirling numbers of the first kind

1991
The authors give a new proof, based on independent discrete random variables, for two known representations of Stirling numbers of the first kind. The proof is based on a recursive formula, and the authors utilize a sequence of independent discrete random variables.
YAMATO, Hajime, FUJISAKI, Tsunehiro
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Theory and applications of Stirling's numbers of the first kind

1983
Bibliography: p. 108-111.
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Asymptotic Development of the Stirling Numbers of the First Kind

Journal of the London Mathematical Society, 1958
Moser, L., Wyman, M.
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The Stirling Numbers of the First Kind

2006
Khee Meng Koh, Eng Guan Tay
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Free piston Stirling engines: A review

International Journal of Energy Research, 2020
Alireza Tavakolpour-Saleh, Shahryar Zare   +1 more
exaly  

Convolution identities for Stirling numbers of the first kind via involution

Integers, 2012
Summary: The author provides bijective proofs of some recent convolution identities for the Stirling numbers of the first kind, which were proven earlier using algebraic methods, by defining appropriate sign-changing involutions.
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