有界区域的Ccy积分公式 设f(z)是区域G中的单值解析函 数,G的边界C是分段光滑曲线, a为G内一点,则 f(a) 1f(z) d 27Ti 其中积分路线沿C的正向 此结果应与T的大小无关 f(a) f(2) m 2- z-0=T -
Cauchy Integral Formula Higher-order Derivatives of ... Integral as Function of Parameter Involved Cauchy Integral Formula: Finite Domain Cauchy Integral Formula: Infinite Domain k.«CauchyÈ©úª f(z)´«G¥ü)Û¼ ê§G>.C´©ã1w§ aGS:§K f(a) = 1 2πi I C f(z) z − a dz ٥ȩ´÷C d(JA I rÃ' C f(z) z − a dz = lim r→0 I |z−a|=r f(z) z − a dz C. S. Wu 1Êù ECÈ©()
有界区域的 Cauchy积分公式 设∫(x)是区域G中的单值解析函 数,G的边界C是分段光滑曲线, a为G内一点,则 f(a)= 1f(2) 2-a 其中积分路线沿C的正向 因为m(2-)() 证得 -af(a),由第四讲引理I,就 f(a) TiNc z-a dz= f(a) C. S. Wu
Cauchy Integral Formula Higher-order Derivatives of ... Integral as Function of Parameter Involved Cauchy Integral Formula: Finite Domain Cauchy Integral Formula: Infinite Domain k.«CauchyÈ©úª f(z)´«G¥ü)Û¼ ê§G>.C´©ã1w§ aGS:§K f(a) = 1 2πi I C f(z) z − a dz ٥ȩ´÷C Ïlim z→a (z − a) f(z) z − a = f(a)§d1oùÚnI§Ò y 1 2πi I C f(z) z − a dz = f(a) C. S. Wu 1Êù ECÈ©()
特殊形式 有界区域的 Cauchy积量取C为以为圆心、R为半径 分公式 的圆周,z-a f(a)= 1(f() d- reide dz TtIgz-a
Cauchy Integral Formula Higher-order Derivatives of ... Integral as Function of Parameter Involved Cauchy Integral Formula: Finite Domain Cauchy Integral Formula: Infinite Domain k.«CauchyÈ ©úª f(a) = 1 2πi I C f(z) z − a dz AÏ/ª C±a %!R» ±§z − a = Re iθ dz = Re iθ idθ f(a)= 1 2π Z 2π 0 f a+Re iθ dθ þ½n )Û¼êf(z)3)Û«GS?¿:a¼ê f(a)§ u( uGS)±a %? ±þ¼ê²þ C. S. Wu 1Êù ECÈ©()
特殊形式 有界区域的 Cauchy积量取C为以为圆心、R为半径 分公式 的圆周 f(a)= 1(f() dz= reside dz TtIgz-a
Cauchy Integral Formula Higher-order Derivatives of ... Integral as Function of Parameter Involved Cauchy Integral Formula: Finite Domain Cauchy Integral Formula: Infinite Domain k.«CauchyÈ ©úª f(a) = 1 2πi I C f(z) z − a dz AÏ/ª C±a %!R» ±§z − a = Re iθ dz = Re iθ idθ f(a)= 1 2π Z 2π 0 f a+Re iθ dθ þ½n )Û¼êf(z)3)Û«GS?¿:a¼ê f(a)§ u( uGS)±a %? ±þ¼ê²þ C. S. Wu 1Êù ECÈ©()
特殊形式 有界区域的 Cauchy积量取C为以为圆心、R为半径 分公式 的圆周 f(a)= 1(f() dz= reside dz TtIgz-a 2丌 f(a) 2丌 f(a+Re)do 解析函数f(2)在解析区域G内任意一点a的函数 值f(a),等于(完全位于G内的)以a为圆心的任 圆周上的函数值的平均
Cauchy Integral Formula Higher-order Derivatives of ... Integral as Function of Parameter Involved Cauchy Integral Formula: Finite Domain Cauchy Integral Formula: Infinite Domain k.«CauchyÈ ©úª f(a) = 1 2πi I C f(z) z − a dz AÏ/ª C±a %!R» ±§z − a = Re iθ dz = Re iθ idθ f(a)= 1 2π Z 2π 0 f a+Re iθ dθ þ½n )Û¼êf(z)3)Û«GS?¿:a¼ê f(a)§ u( uGS)±a %? ±þ¼ê²þ C. S. Wu 1Êù ECÈ©()