Results 271 to 280 of about 152,870 (324)
Some of the next articles are maybe not open access.
Aequationes mathematicae
\textit{L. C. Hsu} and \textit{P. J. S. Shiue} [Adv. Appl. Math. 20, No. 3, 366--384 (1998; Zbl 0913.05006)] introduced a far-reaching generalization of Stirling numbers, \(S(n,k;\alpha,\beta,r)\), and they gave eleven known combinatorial sequences as specializations. \textit{B. Bényi} et al. [Integers 22, Paper A79, 28 p.
openaire +2 more sources
\textit{L. C. Hsu} and \textit{P. J. S. Shiue} [Adv. Appl. Math. 20, No. 3, 366--384 (1998; Zbl 0913.05006)] introduced a far-reaching generalization of Stirling numbers, \(S(n,k;\alpha,\beta,r)\), and they gave eleven known combinatorial sequences as specializations. \textit{B. Bényi} et al. [Integers 22, Paper A79, 28 p.
openaire +2 more sources
Log-concavity of stirling numbers and unimodality of stirling distributions
Annals of the Institute of Statistical Mathematics, 1988A 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.
openaire +1 more source
2012
In this chapter we focus on functions of q x , or equivalently functions of the q-binomial coefficients. We systematically find q-analogues of the formulas for Stirling numbers from Jordan and the elementary textbooks by J. Cigler and Schwatt. To this end, various q-difference operators are used. In each of Sections 5.2–5.4, we focus on a certain such △
openaire +1 more source
In this chapter we focus on functions of q x , or equivalently functions of the q-binomial coefficients. We systematically find q-analogues of the formulas for Stirling numbers from Jordan and the elementary textbooks by J. Cigler and Schwatt. To this end, various q-difference operators are used. In each of Sections 5.2–5.4, we focus on a certain such △
openaire +1 more source
Stirling Numbers and Bernoulli Numbers
2014In 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.
Tomoyoshi Ibukiyama, Masanobu Kaneko
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
Cancer treatment and survivorship statistics, 2022
Ca-A Cancer Journal for Clinicians, 2022Kimberly D Miller +2 more
exaly