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By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn+r/(n+rr). 相似文献
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《Journal of Number Theory》2002,97(1):95-112
We examine densities of several sets connected with the Fermat numbers Fm=22m+1. In particular, we prove that the series of reciprocals of all prime divisors of Fermat numbers is convergent. We also show that the series of reciprocals of elite primes is convergent. 相似文献
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Ladislav Skula 《Mathematica Slovaca》2008,58(1):5-10
In this note the sums s(k, N) of reciprocals
are investigated, where p is an odd prime, N, k are integers, p does not divide N, N ≥ 1 and 0 ≤ k ≤ N − 1. Some linear relations for these sums are derived using “logarithmic property” and Lerch’s Theorem on the Fermat quotient.
Particularly in case N = 10 another linear relation is shown by means of Williams’ congruences for the Fibonacci numbers.
Published results were acquired using the subsidization of the Ministry of Education, Youth and Sports of the Czech Republic,
research plan MSM 0021630518 “Simulation modeling of mechatronic systems”. 相似文献
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一类Orlicz空间中复系数多项式的倒数逼近 总被引:1,自引:0,他引:1
定义了互余的N函数M(u)和N(v)的△条件,并研究了由这种N函数M(u)所生成的一类Orlicz空间中复系数多项式的倒数逼近问题. 相似文献
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In this paper,we consider infinite sums of the reciprocals of the Fibonacci numbers.Then applying the floor function to the reciprocals of this sums,we obtain a new identity involving the Fibonacci numbers. 相似文献
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We consider several aspects of the role and evaluation of the four-sexagesimal-place approximation to
on the well-known Old Babylonian tablet YBC 7289. By referring to what is known about OB school texts, we show that this text is most probably a school exercise by a trainee scribe who got the approximation from a coefficient list. These coefficient lists are briefly described, with their use in geometrical problems. We consider other texts involving square roots and derive an algorithm for evaluating them, which complies with all known OB examples, from a simple geometrical construction of the type that seems to underlie many other OB procedures.Copyright 1998 Academic Press.Nous considérons plusieurs aspects du rôle et de l'évaluation de l'approximation à quatre places sexagésimales de
sur cette tablette paléo-babylonienne. En nous référant à l'état des connaissances quant aux textes scolaires paléo-babyloniens, nous montrons comment ce texte est très probablement un exercice scolaire exécuté par un apprenti scribe qui a obtenu l'approximation à partir d'une liste de coéfficients. Nous décrivons en bref ces listes de coéfficients, ainsi que leur utilisation dans les problèmes de géométrie. Nous considérons d'autres textes traitant de racines carrées , et pour les évaluer nous dérivons un algorithme qui est en accord avec tous les exemples paléo-babyloniens connus; ceci à partir d'une construction géométrique simple du type qui semble être charactéristique de beaucoup d'autres procédures paléo-babyloniennes.Copyright 1998 Academic Press.MSC 1991 subject classifications: 01A17; 11-03 相似文献
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Bao-huai Sheng 《应用数学学报(英文版)》2005,21(4):529-536
Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f(x)∈L^p(S^q-1),f(x)≥0,f absohutely unegual to 0,1≤p≤+∞,Then,it is proved in the present paper that there is a spherical harmonics PN(x) of order≤N and a constant C〉0 such that where ω(f,δ)L^p=sup 0〈t≤δ‖St(f)-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω(f,N^-1)L^p,St(f,μ)=1/|S^q-2|Sin^2λt ∫-μμ’=t f(μ')dμ' is a translation operator. 相似文献
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