p-级数的性质与拓展教学研究

On Properties of p-Series and Related Extensive Teaching

总结了高等数学和数学分析教学中p-级数的基本性质,并对其进行了拓展教学的研究.首先指出p-级数的基本性质及其证明过程中体现的重要数学思想.然后在此基础上进一步讨论了p-级数与欧拉常数的关系,p-级数值的实数性质以及p-级数和黎曼函数的关系.通过这些讨论,把p-级数基本性质的教学内容和现代数学前沿的重要问题结合起来,可以为相关内容的教学提供参考.

Basic properties of p‐series and related extensive teaching of High Mathematics and Mathemati‐cal Analysis have been summarized in this paper .First of all ,basic properties of p‐series and important mathematics thought reflected in the proof of them have been given .Then ,based on these results ,some discussion about the relationship between p‐series and Euler constant ,the real number property of the val‐ue of p‐series ,and the relationship between p‐series and Riemann function have been presented ,by which the teaching content of basic properties of p‐series and the important problems of modern mathematics forefront have been combined ,which can provide reference for the related teaching contents .