Series of Complex Function 特别是,令P=1,就得到 级数收敛的必要条件 lim 0 n→o 收敛级数的基本性质 在不改变求和次序的前提下,可将收敛级数并项 1+u2+3+u4+ =(1+u2)+(u3+u4)+
Complex Series Series of Complex Functions Power Series Complex Series: Convergency & Divergency Absolutely Convergency AO´§-p = 1§Ò ?êÂñ7^ lim n→∞ un = 0 Âñ?êÄ 5 3ØUC¦ÚgScJe§òÂñ?ê¿ u1 + u2 + u3 + u4 + · · · = (u1 + u2) + (u3 + u4) + · · · C. S. Wu 18ù á?ê
utely Convergency 讲授要点 ③复数级数 复数级数·收敛与发散 绝对收敛级数 函数级数 函数级数的收敛性 函数级数的一致收敛性 。含参量反常积分的解析性 ③幂级数 Abel定理 收敛圆与收敛半径
Complex Series Series of Complex Functions Power Series Complex Series: Convergency & Divergency Absolutely Convergency ùÇ: 1 Eê?ê Eê?ê • ÂñuÑ ýéÂñ?ê 2 ¼ê?ê ¼ê?êÂñ5 ¼ê?êÂñ5 ¹ëþ~È©)Û5 3 ?ê Abel½n Âñ Âñ» C. S. Wu 18ù á?ê
Series of Complex Function Convergency &e Divergency utely Convergency 绝对收敛级数 若级数∑lun|收敛,则称级数∑un绝对收敛
Complex Series Series of Complex Functions Power Series Complex Series: Convergency & Divergency Absolutely Convergency ýéÂñ?ê e?ê P ∞ n=0 |un|Âñ§K¡?ê P ∞ n=0 unýéÂñ ýéÂñ?ê½Âñ |un+1 + un+2 + · · · + un+p| ≤ |un+1| + |un+2| + · · · + |un+p| < ε §Âñ?ê±ØýéÂñ C. S. Wu 18ù á?ê
Series of Complex Function Convergency &e Divergency utely Convergency 绝对收敛级数 若级数∑lun|收敛,则称级数∑un绝对收敛 ρ绝对收敛级数一定收敛 un+1+un+2+…+tn+ ≤|un+1|+|n+2+…+|un+p|<E 反之,收敛级数可以不绝对收敛
Complex Series Series of Complex Functions Power Series Complex Series: Convergency & Divergency Absolutely Convergency ýéÂñ?ê e?ê P ∞ n=0 |un|Âñ§K¡?ê P ∞ n=0 unýéÂñ ýéÂñ?ê½Âñ |un+1 + un+2 + · · · + un+p| ≤ |un+1| + |un+2| + · · · + |un+p| < ε §Âñ?ê±ØýéÂñ C. S. Wu 18ù á?ê
Series of Complex Function Convergency &e Divergency utely Convergency 绝对收敛级数 若级数∑lun|收敛,则称级数∑un绝对收敛 ρ绝对收敛级数一定收敛 un+1+un+2+…+ Un+p <1un+1 +|un+2|+…+ 反之,收敛级数可以不绝对收敛
Complex Series Series of Complex Functions Power Series Complex Series: Convergency & Divergency Absolutely Convergency ýéÂñ?ê e?ê P ∞ n=0 |un|Âñ§K¡?ê P ∞ n=0 unýéÂñ ýéÂñ?ê½Âñ |un+1 + un+2 + · · · + un+p| ≤ |un+1| + |un+2| + · · · + |un+p| < ε §Âñ?ê±ØýéÂñ C. S. Wu 18ù á?ê