共查询到18条相似文献,搜索用时 78 毫秒
1.
2.
研究了以自然数倒数所构成的一个典型交错级数重排项后所得级数的收敛性及求和问题.证明了当其正项和负项均按由小到大的顺序排列后,每出现r个正项后面接t个负项的排列所得到的级数收敛,并利用幂级数求得了重排项后级数的和. 相似文献
3.
关于条件收敛级数的重排有著名的黎曼定理:如果级数条件收敛,则无论预先取怎样的数B(有穷的或者等于±∞),都可以重新排列这级数的各项,使得重排后的级数具有和数B。本文要证明下面的结果: 如果一个级数条件收敛,则舍去零项后一定可以重新排列成一个发散的交错级数。 相似文献
4.
关于两类狄里克莱级数系数的重排 总被引:1,自引:0,他引:1
研究了两类狄里克莱级数的系数重排后的增长性,得到了全平面和半平面上有限级狄里克莱级数的系数经过重排后级和型保持不变的充要条件. 相似文献
5.
根据幂级数系数重排级不变的充要条件,对比研究了幂级数系数的重排与此级数的和函数的型之间的关系,得到了幂级数系数重排型不变的一些必要条件。 相似文献
6.
本文研究了Dirichlet级数系数的重排与此级数的收敛横坐标的关系.利用Knopp-Kojima的方法,获得了在Knopp-Kojima公式下绝对收敛横坐标保持不变的重排特征. 相似文献
7.
利用级数的重排与Jacobi三重积恒等式,得到三个级数-乘积型恒等式.作为它们的特殊情形,得到几个与Dedekind eta函数相关的展开式. 相似文献
8.
9.
10.
应用Carlitz反演的U(n+1)形式以及级数重排技巧,建立了几个基本超几何级数变换公式的U(n+1)拓广. 相似文献
11.
J. Marshall Ash Sh. T. Tetunashvili 《Proceedings of the American Mathematical Society》2006,134(6):1681-1686
If at each point of a set of positive Lebesgue measure every rearrangement of a multiple trigonometric series square converges to a finite value, then that series is the Fourier series of a function to which it converges uniformly. If there is at least one point at which every rearrangement of a multiple Walsh series square converges to a finite value, then that series is the Walsh-Fourier series of a function to which it converges uniformly.
12.
Necessary and sufficient conditions are found for the almost sure convergence of almost all simple rearrangements of a series
of Banach space valued random variables. The results go back to Nikishin’s well-known theorem on the existence of an almost
surely convergent rearrangement of a numerical random series. An example is also given of a numerical random series with general
term tending to zero almost surely such that this series converges in probability and any its rearrangement diverges almost
surely. 相似文献
13.
The Ramanujan Journal - In terms of Dougall’s $$_2H_2$$ series identity and the series rearrangement method, we establish a symmetric formula for hypergeometric series. Then it is utilized to... 相似文献
14.
The purpose of this paper is to establish several transformation formulae for bivariate basic hypergeometric series by means of series rearrangement technique. From these transformations, some interesting summation formulae are obtained. 相似文献
15.
该文研究了两类幂级数的系数重排后的增长性,得到了平面上和单位圆内有限级幂级数的系数经过重排后其级和型不变的一些充要条件. 相似文献
16.
Extending the Levy-Steinitz rearrangement theorem in ℝ
n
, which in turn extended Riemann’s theorem, Banaszczyk proved in 1990/93 that a metrizable, locally convex space is nuclear
if and only if the domain of sums of every convergent series (i.e. the set of all elements in the space which are sums of
a convergent rearrangement of the series) is a translate of a closed subspace of a special form. In this paper we present
an apparently complete analysis of the domains of sums of convergent series in duals of metrizable spaces or, more generally,
in (DF)-spaces in the sense of Grothendieck.
The research of the first author was partially supported by DGES Project PB97-0333, and the second one by a grant of the Ministerio
de Educatión y Cultura of Spain (Ref: Sab 1995-0736). 相似文献
17.
S. V. Bochkarev 《Mathematical Notes》1968,4(2):618-623
A continuous function is constructed whose Haar-Fourier series, after a definite rearrangement of its terms, diverges almost everywhere. A function is also constructed which has the maximum degree of smoothness in the sense that if its smoothness is increased its Haar-Fourier series becomes unconditionally convergent almost everywhere.Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 211–220, August, 1968. 相似文献
18.
Marion Scheepers 《Journal of Mathematical Analysis and Applications》2002,267(2):418-433
We show that requiring that the set of positions of the positive terms in a conditionally convergent numerical series have asymptotic density provides converses for old rearrangement theorems of Alfred Pringsheim. 相似文献