Isolated Singulari 讨论 ef(z)在C2外不解析 般说来,在C2上有奇点 外圆C2的半径也可以为∞,甚至在∞点也收 敛
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions ?Ø ❹ f(z)3C2 Ø)Û `5§3C2þkÛ: C2»±∞§$3∞: ñ C. S. Wu 1lù )Û¼êLaurentÐm
Isolated Singulari 讨论 6 Laurent展开既有正幂项,又有负幂项
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions ?Ø ❺ LaurentÐmQk§qkK 3 C2S(|z − b| < R2)ýéÂñ§ 3C2S?¿4«¥Âñ§ ¡ Laurent?êKÜ© K3 C1 (|z − b| > R1)ýéÂñ§ 3C1 ?¿4«¥Âñ§ ¡ Laurent?êÌÜ© C. S. Wu 1lù )Û¼êLaurentÐm
Isolated Singulari 讨论 6 Laurent展开既有正幂项,又有负幂项 °正幂项在圆C2内(|z-b<B2)绝对收敛, 在C2内的任意一个闭区域中一致收敛,称 为 Laurent级数的正则部分 负幂项在圆C1外(2一b>B1)绝对收敛 在C1外的任意一个闭区域中一致收敛,称 为 Laurent级数的主要部分
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions ?Ø ❺ LaurentÐmQk§qkK 3 C2S(|z − b| < R2)ýéÂñ§ 3C2S?¿4«¥Âñ§ ¡ Laurent?êKÜ© K3 C1 (|z − b| > R1)ýéÂñ§ 3C1 ?¿4«¥Âñ§ ¡ Laurent?êÌÜ© C. S. Wu 1lù )Û¼êLaurentÐm
Isolated Singulari 讨论 6 Laurent展开既有正幂项,又有负幂项 正幂项在圆C2内(|z-b<R2)绝对收敛, 在C2内的任意一个闭区域中一致收敛,称 为 Laurent级数的正则部分 负幂项在圆C1外(|z-b>B1)绝对收敛, 在C1外的任意一个闭区域中一致收敛,称 为 Laurent级数的主要部分
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions ?Ø ❺ LaurentÐmQk§qkK 3 C2S(|z − b| < R2)ýéÂñ§ 3C2S?¿4«¥Âñ§ ¡ Laurent?êKÜ© K3 C1 (|z − b| > R1)ýéÂñ§ 3C1 ?¿4«¥Âñ§ ¡ Laurent?êÌÜ© C. S. Wu 1lù )Û¼êLaurentÐm
Isolated Singulari 讨论 6 Laurent展开既有正幂项,又有负幂项 两部分合起来,就构成 Laurent级数,在环域 R1<|z-b<B2内绝对收敛,在环域内的任 意一个闭区域中一致收敛 当R1=0时, Laurent级数的主要部分就完全 反映了f(2)在:=b点的奇异性
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions ?Ø ❺ LaurentÐmQk§qkK üÜ©Üå5§Ò¤Laurent?ê§3 R1 < |z − b| < R2SýéÂñ§3S? ¿4«¥Âñ R1 = 0§Laurent?êÌÜ©Ò N f(z)3z = b:ÛÉ5 C. S. Wu 1lù )Û¼êLaurentÐm