展开定理( Laurent) f()=∑a(2-)B<|=<B2 f() 2πie(x-b)n+1 dc 将两部分合并起来,就有 f(2)=∑an(2-b)(R1<|z-b<B2) 2或 积分路径统一写成了C,为什么 第八讲解析函数的 Laurent
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions Ðm½n(Laurent) (:) f(z)= X∞ n=−∞ an(z−b) n R1 <|z−b|<R2 an = 1 2π i I C f(ζ) (ζ−b) n+1 dζ òüÜ©Ü¿å5§Òk f(z) = X ∞ n=−∞ an(z−b) n (R1<|z−b|<R2) an = 1 2π i I C f(ζ) (ζ−b) n+1dζ È©´»Ú¤ C§oUùº C. S. Wu 1lù )Û¼êLaurentÐm
展开定理( Laurent) f()=∑a(2-)B<|=<B2 f() 2πie(x-b)n+1 dc 将两部分合并起来,就有 f(2)=∑an(2-b)(R1<|z-b<B2) 2或 积分路径统一写成了C,为什么能这样? 第八讲解析函数的 Laurent
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions Ðm½n(Laurent) (:) f(z)= X∞ n=−∞ an(z−b) n R1 <|z−b|<R2 an = 1 2π i I C f(ζ) (ζ−b) n+1 dζ òüÜ©Ü¿å5§Òk f(z) = X ∞ n=−∞ an(z−b) n (R1<|z−b|<R2) an = 1 2π i I C f(ζ) (ζ−b) n+1dζ È©´»Ú¤ C§oUùº C. S. Wu 1lù )Û¼êLaurentÐm
Isolated Singulari 讨论 O Laurent,展开的条件也可以放宽为f(z)在环形区 域B1<|z-b<R2内单值解析即可 e Laurent展开的系数(即使是正幂项的系数
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions ?Ø ❶ LaurentÐm^±°f(z)3/« R1<|z−b|<R2Sü)Û= ❷ LaurentÐmXê(=¦´Xê) an 6= 1 n! f (n) (b) C. S. Wu 1lù )Û¼êLaurentÐm
Isolated Singulari 讨论 O Laurent,展开的条件也可以放宽为f(z)在环形区 域B1<|z-b<R2内单值解析即可 2 Laurent展开的系数(即使是正幂项的系数) 1 n/vn
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions ?Ø ❶ LaurentÐm^±°f(z)3/« R1<|z−b|<R2Sü)Û= ❷ LaurentÐmXê(=¦´Xê) an 6= 1 n! f (n) (b) C. S. Wu 1lù )Û¼êLaurentÐm
Isolated Singulari 讨论 8f(x)在C1内不解析
Expansion in Laurent Series Isolated Singularities of Uniform Function Analytic Continuation Theorem (Laurent) Illustrative Examples Laurent Expansion: Multivalued Functions ?Ø ❸ f(z)3C1SØ)Û `5§3C1þkÛ: ub:§U´f(z)Û:§U´ f(z))Û: XJb:´C1SÛ:§KC1±Ã §ÂñÒC¤0 < |z − b| < R© ùÒ f(z)3áÛ:bSLaurentÐm C. S. Wu 1lù )Û¼êLaurentÐm