奥帕尔在等价级数理论上的贡献

L.Alpár's Contribution on Theory of Equivalent Series

基于原始文献,利用历史分析和比较的方法,首次研究了奥帕尔在等价级数理论方面的工作及影响.分析了奥帕尔的工作背景,指出图兰的工作是其直接基础;研究了他在泰勒级数及法布尔级数的等价级数理论,深入分析了其数学思想和方法.研究结果表明,奥帕尔对等价级数理论的发展做出了重要贡献,其工作对其他数学家有重要影响.

Based on the original literature,L.Alpár’s Work and influence on theory of equivalent series were studied and evaluated by historical analysis and comparative method.Analyzing the background of his work from a series of papers,we found Alpár made further important contributions to the theory of equivalent series.He found several generalizations of the theorem of Turán concerning power series and later extended them to Faber series too.After profound analysis of his mathematical ideas and methods,we confirmed that Alpár made an important contribution to the development of the theory of equivalent series and also had some significant influence on other mathematicians.