幂级数在收敛区间端点收敛时的性质

Power Series at the Endpoints of Its Interval of Convergence

讨论幂级数及其逐项积分、逐项求导后的级数在收敛区间端点收敛时的若干性质,给出它们之间敛散性的关系,并把连续性和逐项可积性推广到幂级数的收敛域上.

Some properties of a power series at the endpoints of its interval of convergence are discussed. Relations of the endpoints convergences between the power series, its derivative or integration （in the sense of term-by-term） are also investigated. The continuity of a power series and the eligibility of the term-by-term integration are generalized to the domain of convergence.