共查询到19条相似文献,搜索用时 78 毫秒
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党四善 《纯粹数学与应用数学》1998,14(3):60-64,59
采用组合数学的方法,利用第二类Stirling数和Bernouli数给出级数∑∞k=2kmζ(k)、∑∞k=1kmζ(2k)及∑∞k=1(2k+1)mζ(2k+1)(其中m≥1,ζ(x)=ζ(x)-1)的求和公式。这些公式表述简洁并有鲜明的规律性。 相似文献
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设f(n)表示自然数n的乘法分拆数。对于所有奇数,较大地改进了n的系数,证明了:若n为奇数,则f(n)≤n/15 7/5。 相似文献
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Stirling数的概率表示和应用 总被引:8,自引:0,他引:8
本文证明了第二类Stirling数S(n,k)和第一类Stirling数s(n,k)都是常见的随机变量和的矩,从而使概率论的方法和技巧,在组合和式计算、恒等式的发现与证明以及渐近估计等方面得到许多新的结果. 相似文献
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联系Bernoulli数和第二类Stirling数的一个恒等式 总被引:5,自引:0,他引:5
利用指数型生成函数建立起联系Bernoulli数和第二类Stirling数的一个有趣的恒等式. 相似文献
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本文研究了抽球概率模型的问题.利用概率方法,获得了关于第一类Stirling数和广义可重复二项式系数的无限求和形式的组合恒等式以及有关组合解释,推广了Stirling数和二项式系数的无限求和结果. 相似文献
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分堆问题是排列组合中常遇到的难题之一.通过一个易错概率题的分析,推广了分堆问题,定义相同结构,并对相同结构下的排列组合进行研究,给出了相同结构下的计算公式,并利用离散型随机变量的性质加以验证.此外,还发现了一个符号运算的恒等式,并进行了证明. 相似文献
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三类与Riemann Zeta函数有关的级数的求和公式 总被引:4,自引:0,他引:4
本文采用组合数学的方法,利用第二类Stirling数和Bernoulli数给出级数∑∞k=2k^mξ(2k)及∑∞k=1(2k+1)^mξ(2k+1)其中m≥1,ξ(x)=ξ(x)-1)的求和公式。这些公式表述简洁并有鲜明的规律性。 相似文献
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John S. Caughman Charles L. Dunn Nancy Ann Neudauer Colin L. Starr 《Discrete Mathematics》2011,(16):1803
Lattice chains and Delannoy paths represent two different ways to progress through a lattice. We use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in a lattice of arbitrary finite dimension. Specifically, fix nonnegative integers n1,…,nd, and let L denote the lattice of points (a1,…,ad)∈Zd that satisfy 0≤ai≤ni for 1≤i≤d. We prove that the number of chains in L is given by where . We also show that the number of Delannoy paths in L equals Setting ni=n (for all i) in these expressions yields a new proof of a recent result of Duchi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension. 相似文献
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Two statistics with respect to “upper-corners” and “lower-corners” are introduced for lattice paths. The corresponding refined generating functions are shown to be closely related to the q-ballot polynomials that extend the well-known Narayana polynomials and Catalan numbers. 相似文献
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放缩,反演和障碍问题 总被引:1,自引:0,他引:1
代替移动平面法和滑动区域法,作者利用放缩和反演变换研究某些半线性椭圆型分分下等方程解的单调性和对称性,这些变换依赖某一参数,在关于数据的单调性的适当假定下,当参数近某一初始值最大值时,解和其变换的差在某一“窄区域”满足一个椭圆型不等式,利用Varadhan的极值原理,即得这个差是正的并得到解的单调性。 相似文献
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We suggest an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., we give an explicit continuation formula and a regularization procedure for a solution to the Cauchy problem for the Laplace equation. 相似文献
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Occupancy distributions are defined on the stochastic model of random allocation of balls to a specific number of distinguishable
urns. The reduction of the joint distribution of the occupancy numbers, when a specific number of balls are allocated, to
the joint conditional distribution of independent random variables given their sum, when the number of balls allocated is
unspecified, is a powerful technique in the study of occupancy distributions. Consider a supply of balls randomly distributed
into n distinguishable urns and assume that the number X of balls distributed into any specific urn is a random variable with probability function P(X = x) = q
x
, x = 0, 1,.... The probability function of the number L
r
of occupied urns until r balls are placed into previously occupied urns is derived in terms of convolutions of q
x
, x = 0, 1,... and their finite differences. Further, using this distribution, the minimum variance unbiased estimator of the
parameter n, based on a suitable sequential sampling scheme, is deduced. Finally, some illustrating applications are discussed.
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