Results 281 to 290 of about 149,574 (327)

Stirling Numbers for Complex Arguments

SIAM Journal on Discrete Mathematics, 1997
The authors define the Stirling numbers for the case of a complex argument by invoking the Cauchy integral formula. Some of the usual identities extend, but others do not. The properties of unimodality and monotonicity do extend.
B. RICHMOND, MERLINI, DONATELLA
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Stirling Numbers and Eulerian Numbers

2016
This chapter is dedicated to counting partitions of sets and partitions of sets into cycles, and also introduces Stirling numbers and Bell numbers. As an application of the concepts discussed here we state Faa di Bruno chain rule for the n-th derivative of a composite of n-times differentiable functions on \(\mathbb R\).
Carlo Mariconda, Alberto Tonolo
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A Generalization of the S-Stirling Numbers

Mathematics Magazine, 1956
Introduction: the purpose of this paper is to develope a general formula for the S-Stirling numbers by the use of poly-gama functions. Since the poly-gamma functions have meaning also for non-integer values, we can take the resulting expression for the S-Stirling numbers as their definition.
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Log-concavity of stirling numbers and unimodality of stirling distributions

Annals of the Institute of Statistical Mathematics, 1988
A series of inequalities involving Stirling numbers of the first and second kind with adjacent indices are obtained, some of which show log- concavity of Stirling numbers in three directions. Some of them are new, others extend or improve earlier results.
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The Arithmetic of Bell and Stirling Numbers

American Journal of Mathematics, 1948
Symbolic methods are used to obtain many of the properties of the Bell and Stirling numbers [cf. \textit{E. T. Bell}, Am. J. Math. 61, 89--101 (1939; Zbl 0020.10402)] modulo \(p\), a prime.
H. W. Becker, John Riordan
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Stirling Numbers and Records

1997
Stirling numbers and generalized Stirling numbers and their properties are briefly described first. Then some relationships between Stirling numbers and record times are presented. Finally, we show that generalized Stirling numbers of the first kind describe distributions of some record statistics in the so-called Fα-scheme.
N. Balakrishnan, V. B. Nevzorov
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Stirling Numbers and Bernoulli Numbers

2014
In this chapter we give a formula that describes Bernoulli numbers in terms of Stirling numbers. This formula will be used to prove a theorem of Clausen and von Staudt in the next chapter. As an application of this formula, we also introduce an interesting algorithm to compute Bernoulli numbers.
Masanobu Kaneko, Tomoyoshi Ibukiyama
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Cancer treatment and survivorship statistics, 2022

Ca-A Cancer Journal for Clinicians, 2022
Kimberly D Miller, Leticia M Nogueira, Angela B Mariotto   +2 more
exaly  

Stirling Numbers

1983
George Pólya, Robert E. Tarjan, Donald R. Woods   +2 more
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Proportion and number of cancer cases and deaths attributable to potentially modifiable risk factors in the United States

Ca-A Cancer Journal for Clinicians, 2018
Farhad Islami, Ann Goding Sauer Msph, Kimberly D Miller   +2 more
exaly