两个幂级数和的收敛半径

Convergence Radius of the Sum of Two Power Series

基于幂级数的性质和收敛半径的计算公式,利用Heine定理和洛必达法则,讨论了当幂级数∑∞n=0a_nx^n和∑∞n=0b_nx^n的收敛半径相等,极限lim n→∞a_n/b_n取不同值时,计算收敛半径的一些充分条件,进一步丰富了幂级数运算的理论。

Basedon properties and calculation formulas for convergence radius of power series, some sufficient conditions for calculations of the convergence radius of∞∑N=0 （ an ＋ bn） xn with different limitantion lim n→∞an/bn are obtained by using Heine Theoryand L Hospital Rules , where the convergence radiusesn of power series ∞∑N=0 anxn and ∞∑N=0 bnx n are equal. The results can further enrich theories of power series operations.