共查询到20条相似文献,搜索用时 72 毫秒
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On the Distribution of Weakly Composite Numbers 总被引:1,自引:0,他引:1
OntheDistributionofWeaklyCompositeNumbers王天泽,李国强OntheDistributionofWeaklyCompositeNumbers¥WangTianze;LiGuoqiang(DepartmentofM... 相似文献
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TheNumbersofPermutationGroupsOrbitsandoftheWreathProductOrbits¥LiXianzhong;LiuGuangliang(PuyangEducationalCollege,Henan,45700... 相似文献
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By using small function method, the following result is obtained. If f(z) is transcendental meromorphic and that Ψ(z) is non-zero meromorphic and that T(r, Ψ) =S(r, f), then (n 1)T(r,f)≤(-N)(r,1/f'fn-Ψ) 2(-N)(r,1/f) (-N)(r,f) S(r,f). 相似文献
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Xiao Qian WANG Shi Hong CHENG 《数学学报(英文版)》2005,21(5):1121-1130
In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved. 相似文献
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B. FISHER K. TAS 《数学学报(英文版)》2006,22(6):1639-1644
Let f and g be distributions and let gn = (g * δn)(x), where δn (x) is a certain converging to the Dirac delta function. The non-commutative neutrix product fog of f and g to be the limit of the sequence {fgn }, provided its limit h exists in the sense that sequence is defined N-lim n-∞(f(x)g,, (x), φ(x)〉 = (h(x), φ(x)},for all functions p in 2. It is proved that (x^λ+1n^px+)0(x^μ+1n^qx+)=x+^λμ1n^p+qx+,(x^λ-1n^qx-)=x-^λ+μ1n^p+qx-,for λ+μ〈-1; λ,μ, λ+μ≠-1,-2…and p,q=0,1,2…… 相似文献
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Andreas George Kyriakoussis Malvina Vamvakari 《Methodology and Computing in Applied Probability》2013,15(1):187-213
In this article, we derive an asymptotic formula for the q-factorial number of order n using the saddle point method. This formula is a q-analogue, for 0?<?q?<?1, of the usual Stirling formula for the factorial number of order n. Also, this formula is used to provide a continuous limiting behaviour of the q-Binomial distribution in the sense of pointwise convergence. Specifically, the q-Binomial distribution converges to a continuous Stieltjes–Wigert distribution. Furthermore, we present some numerical calculations, using the computer program MAPLE, indicating a quite strong convergence. 相似文献
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Huixue LAO 《数学年刊B辑(英文版)》2010,31(3):385-392
The author uses analytic methods to study the distribution of integral ideals and Hecke Grossencharacters in algebraic number fields. Nowak's results on the distribution of integral ideals, and Chandrasekharan and Good's results on the distribution of Hecke GrSssencharacters are improved. 相似文献
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Mario DeFranco 《Journal of Difference Equations and Applications》2013,19(9):1101-1120
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 numbers given by Adamchik (1997, J. Comput. Appl. Math., 79). We also see a connection to the Riemann zeta function. 相似文献
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Christian Elbert 《Journal of Approximation Theory》2001,109(2):708
For the horizontal generating functions Pn(z)=∑nk=1 S(n, k) zk of the Stirling numbers of the second kind, strong asymptotics are established, as n→∞. By using the saddle point method for Qn(z)=Pn(nz) there are two main results: an oscillating asymptotic for z(−e, 0) and a uniform asymptotic on every compact subset of
\[−e, 0]. Finally, an Airy asymptotic in the neighborhood of −e is deduced. 相似文献
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第二类Stirling数的一个公式 总被引:1,自引:0,他引:1
In this paper, We propose and prove the following equation, where is a Stirling number of the second kind, when n≥3 is given. 相似文献
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利用概率论与组合数学的方法,研究了与Riemann-zeta函数ξ(k)的部分和ξ_n(k)有关的一些级数,计算出了一些重要的和式.特别的,Euler的著名结果5ξ(4)= 2ξ~2(2)能够从四阶和式直接推出.因此,通过计算全部的11个六阶和式,研究它们之间的非平凡关系,就有可能得到ξ(3)的数值. 相似文献
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通过计算两个广义的范德蒙(Vandermonde)行列式,得到了第一类无符号Stirling数和第二类Stirling数的一种新的表示方法:用行列式来表示. 相似文献
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利用第一、二类高阶Bernoulli数和二类Stirling数S1(n,k),S2(n,k)的定义.研究了二类高阶Bernoulli数母函数的幂级数展开,揭示了二类高阶Bernoulli数之间以及与第一类Stirling数S1(n,k)、第二类Stirling数S2(n,k)之间的内在联系,得到了几个关于二类高阶Bernoulli数和第一类Stirling数S1(n,k)、第二类Stirling数S2(n,k)之间有趣的恒等式. 相似文献
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A multiplication theorem for the Lerch zeta function ?(s,a,ξ) is obtained, from which, when evaluating at s=−n for integers n?0, explicit representations for the Bernoulli and Euler polynomials are derived in terms of two arrays of polynomials related to the classical Stirling and Eulerian numbers. As consequences, explicit formulas for some special values of the Bernoulli and Euler polynomials are given. 相似文献
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