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

Abstract:

      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.