对波莱尔关于“泰勒展开一般以收敛圆为割线”思想研究

E.Borel's Thought on the Claim ``Taylor Series Generally Considers Its Convergent Circle as the Cut Secant''

中文关键词:  泰勒展开  函数奇点  解析开拓.

英文关键词:Taylor development  function singularities  analytic continuation.

中文摘要:

      “泰勒展开是否以收敛圆为割线”问题是解析开拓理论研究的重要课题,但对此国内外尚无全面细致地研究. 鉴于此，以原始资料为依据，围绕法国数学家波莱尔(E.Borel)关于此方面的工作,分析了波莱尔关于“泰勒展开一般以收敛圆为割线”的思想来源,探讨了其思想的演变过程和在当时及以后的重要影响.

英文摘要:

      The research on that ``Taylor series generally considers its convergent circle as the cut secant'' is an important problem of analytic continuation. This paper analyzes E.Borel's mathematic work relative to the research of this problem by the method of historical proof. His work on this problem is not studied at present. This paper discusses his background thought, the development of his idea and the influence on other mathematicians at that time.