共查询到18条相似文献,搜索用时 46 毫秒
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对于所有的整数n≥0,Landau常数定义为Gn=nΣk=01/16k(2kk)2.该文建立了Landau常数新的逼近公式.指出了获得的结果与先前已有结果之间的相关联系 相似文献
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陈超平张小 《数学的实践与认识》2021,(17):298-304
证明了4√xarcsin(√x/2)/(4-x)3/2+4/4-x=(∞∑n=0)1/(2nn)xn,丨x丨<4.选择x = 2得到常数π的级数表示式π/2 =∑∞n=22n/(2nn).基于这个表示式,建立了余项Rn= π/2-∑nk=22k/(2kk)的渐近展开式,然后给出了Rn的上下界.作为应用,给出了常数π的近... 相似文献
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函数的渐近级数展开式与收敛级数展开式是解决非线性问题的有力工具.本文剖析了这两类展开式的特性、分析了它们的区别等,在此基础上对如何准确有效地使用这两类展开式进行了探讨. 相似文献
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对于所有的整数n≥0,Landau常数和Lebesgue常数分别定义为G_n=∑nk=01/16~k(2k/k)~2和L_n=1/2π∫_(-π)~π|sin((n+1/2)t)/sin(1/2t)|dt.本文给出G_n和L_(n/2)新的渐近级数.基于获得的结果,本文建立了Landau常数和Lebesgue常数新的不等式.设f∈C[-1,1],(s_nf)(x)=∑_(k=0)~na_kT_k(x)是f的Chebyshev展开式的部分和.Cheney指出,对于所有直到400为止的n值,当用最佳多项式逼近替代s_nf时,精度至多提高一位十进小数.本文证明了Cheney的论断对于n≤191833603亦真,而且本文说明了191833603不能被更大的整数替代. 相似文献
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在级数敛散性的判别中,广级数有着举足轻重的作用,它是一个典型级数。本文将给出户级数部分和的估计式由此得出一个很重要的常数—Euler常数。一、P级数部分和的估计式考虑函数y=x-P(P>0,X>0),计算其一、二阶导数y’=px-1<0;y”=p(p 1)x-p-2>0,即函数y=xp的图形是单调减小、凹的(如图)。以下来估计在区间二,。」上曲边梯形的面积卜一’d。。由于},一。’的图形是凹的,由定积分近似计算中的梯形法公式知,其诸梯形面积之和应大于曲边梯形面积。图中以[k-l,hi为底边,上为高的n-l个矩形。积之。应小,曲。梯形面积… 相似文献
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Cristinel Mortici 《Applied mathematics and computation》2010,215(9):3443-919
We propose new simple sequences approximating the Euler-Mascheroni constant and its generalization, which converge faster towards their limits than those considered by DeTemple [D.W. DeTemple, A quicker convergence to Euler’s constant, Am. Math. Monthly 100 (5) (1998) 468-470], Sînt?m?rian [A. Sînt?m?rian, A generalization of Euler’s constant, Numer. Algorithms 46 (2) (2007) 141-151] and Vernescu [A. Vernescu, A new accelerate convergence to the constant of Euler, Gazeta Matem., Ser. A, Bucharest XVII(XCVI) (4) (1999) 273-278]. 相似文献
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Harun Karsli 《Numerical Functional Analysis & Optimization》2013,34(11):1206-1223
The purpose of this article is to study the local rate of convergence of the Chlodovsky operators (Cnf)(x). As the main results, we investigate their asymptotic behaviour and derive the complete asymptotic expansions of these operators. All the coefficients of n?k (k = 1, 2,…) are calculated in terms of the Stirling numbers of first and second kind. We mention that analogous results for the Bernstein polynomials can be found in Lorentz [2]. 相似文献
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Subhashis Ghosal Tapas Samanta 《Annals of the Institute of Statistical Mathematics》1997,49(1):181-197
We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment. 相似文献
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具体计算了球面Sn(1)(n2)上热核的渐近展开式中前五项的系数,而根据已有的公式只能算出前四项.最后给出了展开式一般项的递推公式,发现它与Bernouli数有未曾想到的联系.根据不变量理论,我们可以确定任意n维紧致无边Riemann流形上热核的渐近展开式中第五项的系数. 相似文献
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对于慢收敛多重级数Ik=∑ from (n1,n2,…,nk=1) to ∞((-)1~nlnn/n|n=n1+n2+…+nk,利用渐近展开方法给出闭形式. 相似文献
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《复变函数与椭圆型方程》2012,57(1):81-87
Chen, Gauthier and Hengartner obtained some versions of Landau's theorem for bounded harmonic mappings and Bloch's theorem for harmonic mappings which are quasiregular and for those which are open. Later, Dorff and Nowak improved their estimates concerning Landau's theorem. In this study, we improve these last results by obtaining sharp coefficient estimates for properly normalized harmonic mappings. Furthermore, our estimates allow us to improve Bloch constant for open harmonic mappings. 相似文献
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Ryoichi Shimizu Yasunori Fujikoshi 《Annals of the Institute of Statistical Mathematics》1997,49(2):285-297
Let Z be a random variable with the distribution function G(x) and let s be a positive random variable independent of Z. The distribution function F(x) of the scale mixture X = sZ is expanded around G(x) and the difference between F(x) and its expansion is evaluated in terms of a quantity depending only on G and the moments of the powers of the variable of the form s/gr - 1, where (> 0) and (= ±1) are parameters indicating the types of expansion. For = -1, the bound is sharp under some extra conditions. Sharp bounds for errors of the approximations of the scale mixture of the standard normal and some gamma distributions are given either by analysis ( = -1) or by numerical computation ( = 1). 相似文献