正项级数敛散性的对数判别法与拉贝判别法

研究正项级数的敛散性判定的对数判别法与拉贝判别法.首先给出了定理与推论,然后给出了证明,最后举例说明它们的应用.     

正项级数的Raabe对数判别法

在正项级数敛散性Raabe判别法和第一对数判别法的基础上,以P-级数作为比较标准,讨论了第二对数判别法,并且证明了Raabe判别法和第二对数判别法的等价性.     

谈谈几种正项级数敛散性判别法的比较

谈谈几种正项级数敛散性判别法的比较高军（安徽阜阳教育学院２３６０１６）贵刊近年来刊登了几篇有关正项级数敛散性判别法的文章，笔者读后很受启发，并将文［１］与文［２］中所给的两个判别法分别与传统的拉阿贝（Ｒａａｂｅ）和高斯（Ｇａｕｓｓ）判别法进行了比较，...     

一种反常积分与正项级数收敛的判别法

介绍一种判别无穷限反常积分与正项级数敛散性的判别法。     

比较判别法在级数收敛性判别上的应用

本文列举了比较判别法在级数收敛性判别中的几个典型应用,对此方法的常用技巧进行了归纳总结.     

正项级数的广义Cauchy判别法

本文提出了正项级数∞∑n=1a_n新的敛散性判别法,部分解决了根值判别法limn→∞(a_n)~(1/n)=1的遗留问题,即limn→∞(a_n)~(1/n)=1时的判别方法.     

正项级数收敛性的一种新的判别法

将正项级数收敛性的 D′Alembert比值判别法和 Cauchy根值判法的数学思想融合到一起 ,利用正项级数的比较判别法和级数的某些基本性质 ,给出了正项级数收敛性的一种新的判别法 ,暂时称之为 Z-判别法 .     

正项级数的D-C判别法

本文将正项级数的比值审敛法 (达朗贝尔 D' Alembert判别法 )和根值审敛法 (柯西 Cauchy判别法 )结合起来 ,得到正项级数的一个新的审敛法 ,且称之为 D-C判别法 .     

正项级数判敛的一种新的比值判别法

本文给出了正项级数收敛性的一种新的比值判别法。这种判别法强于达朗贝尔比值判别法,且使用方便。为推导新的比值判别法,先证下面的引理。     

正项级数的Gauss指标判别法

在正项级数Gauss判别法的基础上,定义了正数列an的Gauss指标G=lim[n ln(an/an+1)-1]ln n.从而得到了正项级数的Gauss指标判别法.通过具体计算已有各种判别法的Gauss指标,结果表明,Gauss指标判别法是达朗贝尔、柯西、拉贝、高斯和Bertrand等5种判别法的推广.     

Gauss's contributions to statistics

An expository account is given of Gauss's contributions to the statistical theory of estimation. These are known generally under the name of least squares, although this gives little idea of their scope. The magnitude of Gauss's results is discussed in relation to modern theoretical statistics and to the analysis of data in modern experimental science. The logical aspects are emphasized in the light of current work in the area of estimation.     

A Test for Nonlinearity of Time Series with Infinite Variance

A heavy tailed time series that can be represented as an infinite moving average has the property that the sample autocorrelation function (ACF) at lag h converges in probability to a constant (h), although the mathematical correlation typically does not exist. For many nonlinear heavy tailed models, however, the sample ACF at lag h converges in distribution to a nondegenerate random variable. In this paper, a test for (non)linearity of a given infinite variance time series is constructed, based on subsample stability of the sample ACF. The test is applied to several real and simulated datasets.     

正项函数项级数一致收敛的Raabe型判别法的推广

证明了正项函数项级数一致收敛的比值判别法,进而得到了正项函数项级数一致收敛的Raabe型判别法,并给出了应用的实例.     

Certain Classes of Infinite Series

 The authors evaluate some interesting families of infinite series by analyzing known identities involving generalized hypergeometric series. Several special cases of the main results are shown to be related to earlier works on the subject.     

Certain Classes of Infinite Series

 The authors evaluate some interesting families of infinite series by analyzing known identities involving generalized hypergeometric series. Several special cases of the main results are shown to be related to earlier works on the subject. Received 16 December 1996; in revised form 21 May 1997     

Statistical Convergence of Infinite Series

In this paper we use the notion of statistical convergence of infinite series naturally introduced as the statistical convergence of the sequence of the partial sums of the series. We will discuss some questions related to the convergence of subseries of a given series.     

无穷级数引入的教学设计

给出针对无穷级数引入的一种教学设计.以趣味故事作为实例引入,通过对π的计算这个实际问题的讲解,让学生抓住概念的本质,并对无穷级数的应用有一个初步的了解,从而对无穷级数有一个总体的认识.在教学过程中,步步引导,全程既具有趣味性又具有启发性.