共查询到19条相似文献,搜索用时 62 毫秒
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选择p-级数作为参照级数,由比较判别法可得关于交错级数敛散性判别的一种新方法.新方法可直接判别交错级数的敛散性,并在收敛时,给出级数是条件收敛还是绝对收敛.实例说明其应用. 相似文献
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莱布尼兹判别法只是一个充分条件。有大量交错级数虽然不满足其条件,但却是收敛的.对于无法用莱布尼兹判别法判定的三类交错级数,利用常数项级数收敛的定义及相关结果,可以证明在一定条件下它们都是收敛的.并通过实例说明所得结果的应用价值. 相似文献
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作者曾给出过数项级数敛散性的判别程序,本文对原有框图进行了修改和补充.从框图中不仅可以了解到级数收敛的定义,级数收敛的必要条件、交错级数的莱布尼兹定理以及绝对收敛与收敛的关系,更能体会到正项级数在数项级数中的重要地位.事实上,对一般的级数,如果用正项级数的比值或根值审敛法判定收敛,则收敛;若发散,则发散(只要注意到比值或根值审敛法的证明过程就不难推出这一点).正是由于这个原因,正项级数在函数项级数的研究中起着十分重要的作用.一、数项级数敛散性的判别程序二、止坝级数在由数坝线教甲同作用众所周知,定… 相似文献
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倪培溉 《数学的实践与认识》2006,36(3):292-294
“数列xnm~rnm+p审敛原理”,是数列柯西审敛原理的等价命题.采用“数列xnm~rnm+p审敛原理”判别数列(或数项级数)的敛散性比采用柯西审敛原理更便捷;“数列xnm~rnm+p审敛原理”推广了已有的判别数列(或数项级数)敛散性法则,扩大了已有的判别数列(或数项级数)敛散性法则的应用范围. 相似文献
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交错级数的对数判别法 总被引:1,自引:0,他引:1
从正项级数的Raabe对数判别法入手,给出了交错级数的一个新的审敛方法.与文[1],[2]所给的审敛法相比,当交错级数的一般项含有幂指项时,利用该审敛法判断其敛散性显得尤为简便. 相似文献
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通过实例考察常数项级数收敛和发散时一般项的一些特点,并讨论级数不满足比值判别法、根值判别法或莱布尼茨定理的条件时的收敛性问题. 相似文献
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关于交错级数的审敛准则的改进和推广 总被引:2,自引:1,他引:1
讨论了交错级数的敛散性,改进了[1]中关于交错级数新的审敛准则,并给出了交错级数另外新的审敛准则,并将这些审敛准则推广到更一般的形式. 相似文献
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We establish a criterion for the logarithm of the maximal term of a Dirichlet series absolutely convergent in the half-plane to be equivalent on an asymptotic set to the logarithm of the maximal term of its Hadamard composition with any other Dirichlet series from a certain class. 相似文献
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Paolo Amore 《Journal of Mathematical Analysis and Applications》2006,323(1):63-77
By means of a variational approach we find new series representations both for well-known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar exponentially convergent series for a large class of mathematical functions. 相似文献
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In this paper the convergence behavior of the Shannon sampling series is analyzed for Hardy spaces. It is well known that
the Shannon sampling series is locally uniformly convergent. However, for practical applications the global uniform convergence
is important. It is shown that there are functions in the Hardy space such that the Shannon sampling series is not uniformly
convergent on the whole real axis. In fact, there exists a function in this space such that the peak value of the Shannon
sampling series diverges unboundedly. The proof uses Fefferman’s theorem, which states that the dual space of the Hardy space
is the space of functions of bounded mean oscillation.
This work was partly supported by the German Research Foundation (DFG) under grant BO 1734/9-1. 相似文献
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N. S. Moreva 《Mathematical Notes》2007,81(3-4):518-528
We consider uniqueness problems for multiple Walsh series convergent on binary cubes on a multidimensional binary group. We find conditions under which a given finite or countable set is a set of uniqueness. 相似文献