共查询到20条相似文献,搜索用时 15 毫秒
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研究了等差项乘积∏ni=1a_i的渐进估计.首先给出了一系列关于等差项乘积的不等式,继而应用Euler-Maclaurin求和公式及Γ函数的Stirling公式:Γ(x+1)~(2πx)~(1/2)(x/e)~x(x→+∞),推导出了∏ni=1a_i的较精确的渐进式,最后,得到了精确化的Wallis公式. 相似文献
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R. M. Trigub 《Mathematical Notes》1997,61(2):253-257
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Chaweng Changchit
M. Palmer Terrell
《Applied Mathematical Modelling》1990,14(12):641-648In the ceramic field the process of forming a ceramic body consists of several steps that must be executed efficiently and controlled closely to achieve the desired product. A major step in the process is the selection of raw materials, which not only will provide the necessary oxides, but also will melt and fine well to form a high-quality product. This process, if carried out on a trial-and-error manner, may lead to an uneconomical production cost due to wrong materials being selected. In addition, some important physical batch characteristics may be ignored owing to the increase in computational requirements if more constraints are added to the process. In this paper we propose the mathematical modelling approach, which has gained very little attention from researchers in this field, as an alternative to the trial-and-error approach. The model presented in this paper may be used to calculate the batch formula of a designed product without first knowing its empirical formula. An illustrated example of the use of this model is also provided. 相似文献
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齐玉霞 《数学的实践与认识》2010,40(16)
证明了∫_0~(π/2)sin~αxdx(α→+∞)渐进展开式的存在性,并给出了展开式系数的递推公式,进而得到了((2n-1)!!)/((2n)!!)/((2n)!!)的渐进展开式和精致化的Wallis公式.在精致化的Wallis公式中取到1/n~m项,对π的逼近精度可达O(1/(n~(m+1))),比原来的Wallis公式的精度大为提高. 相似文献
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就Green公式、GBUSS公式和Stokes公式这一教学中的重点和难点问题,针对传统的教学方法对积分区域进行"补"或"挖"处理的不足,探讨使用变换的思想从变换的角度来讲解三大定理的应用,揭示定理的核心问题,以便帮助学生理解和掌握. 相似文献
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We give a recursive algorithm to compute the multivariable Zassenhaus formula e^X1+X2+…+Xn=e^X1eX2…e^Xn∏∞k=2e^Wk and derive an effective recursion formula of Wk. 相似文献
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A further combinatorial study of Entries 16 and 17 in chapter 3 of Ramanujan's second notebook [1] leads to a refinement of Cayley's formula for counting trees and generalizes the recent results derived by Shor [13], and Dumont and Ramamonjisoa [5]. Our approach also yields a new proof of Clarke's extension of Cayley's formula [4]. 相似文献
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本文讨论高等数学课程中,高斯公式、格林公式和牛顿-莱布尼兹公式之间的内在联系,指出格林公式和牛顿-莱布尼茨公式可以分别看作一维和二维欧氏空间中的高斯公式.实际上,n维欧氏空间中的高斯公式可以看作微积分基本定理在高维欧氏空间中的表述形式.利用高斯公式还可以导出定积分、二重积分和任意n重积分的分部积分公式. 相似文献
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Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions
Yu. Netrusov 《Journal of Functional Analysis》2007,250(1):21-41
We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L1-function. These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula. 相似文献
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Allan Fryant 《Proceedings of the American Mathematical Society》1996,124(7):2001-2004
An addition formula for homogeneous polynomials is used to obtain a generalization of the Pythagorean theorem and a new view of the multinomial expansion.
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三种不同意义下的最佳求积公式之间的关系 总被引:2,自引:0,他引:2
详细讨论了函数类KWr[a,b]上Sard和N iko lsk ii意义下以及基于给定信息的最佳求积公式三者之间的关系,并且提供了一种由基于给定信息的最佳求积公式得到其它两种求积公式的方法. 相似文献
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杨明顺 《数学的实践与认识》2009,39(10)
由Riemannζ函数的函数方程得到Hurwitzζ函数的Hermite公式,再从Hermite公式得到Γ(s)的Binet′s第二表达式,从而由ζ函数推得Γ(s)的性质. 相似文献
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Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, Mathematics and Computer Education, 39(3), 198–205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry, calculus, and linear algebra. In this paper, this study is generalized further to develop a few interesting case study proposals that can be used for student projects in college mathematics courses such as real functions, analytic geometry, and complex variables. In addition to using them in individual courses, these studies may also be combined to offer seminars or workshops to college mathematics students. Projects like these are likely to promote student interest and get students more involved in the learning process, and therefore make the learning process more effective. 相似文献
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Vaclav Finek 《Applications of Mathematics》2005,50(4):387-399
The scaling function corresponding to the Daubechies wavelet with two vanishing moments is used to derive new quadrature formulas. This scaling function has the smallest support among all orthonormal scaling functions with the properties M
2 = M
1
2
and M
0 = 1. So, in this sense, its choice is optimal. Numerical examples are given.This work was partially supported by DFG grant GR 1777/2, by the Grant No 201/01/1200 of the CSF, by the grant MSMT 113200007 and by the grant IGS 116/5130/1 of FP TUL. 相似文献
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主要研究了ζ函数的积分表示形式;通过解析数论的研究方法,利用黎曼ζ函数方程,给出了关于赫尔维茨ζ函数的埃尔米特公式,利用埃尔米特公式得出关于Γ函数的比内第二表达式,通过ζ函数得出Γ函数一些性质. 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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Katriel, Rasetti and Solomon introduced a q-analogue of the Zassenhaus formula written as eq(A+B)=eqAeqBeqc2eqc3eqc4eqc5… , where A and B are two generally noncommuting operators and eqz is the Jackson q-exponential, and derived the expressions for c2, c3 and c4. It is shown that one can also write
Explicit expressions for
,
and
are given. 相似文献