5.2 解析函数的有限孤立奇点
Post on 03-Jan-2016
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5.2 5.2.15.2.2 1. 2. 3. 5.2.3 Picard5.3.4 Schwarz
- 5.2.1 5.2 f(z)aK-{a}:0
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5.3 af(z). (1)f(z)a,af(z). (2)f(z)a,af(z)m().. (3)f(z)a,af(z).
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5.2.2 1. 5.3 af(z) (2)(1)f(z)a; (3)f(z)a (1)(2);(2) (3);(3)(1) (1)(2)(1)
- (2)(3):1.27.|f(z)|M(M>0).f(z)a(3)(1):aK-{a}{z| 0
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2.a f(z)=c0,af(z)5.4 f(z)a,af(z)m(1)f(z)a (2)f(z)a(z) a,(a)0
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am(a,g(a)=0). (1)(2): aa,
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(2)(3):aa,(1.28)ag(z),,g(a)=0,ag(z)m.4.17 , .
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1/(z) a(1.28),f(z)a 5.5 f(z)a
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3. 5.6 f(z)a ()af(z) af(z) af(z) af(z) af(z)
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5.7 z=af(z),a,z=a. z=a(z)(),z=a(z)af(z)af(z)af(z).,z=a
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EMBED Equation.3
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5.2.3 Picard() 5.8 af(z),A,,a{zn},,,f(z)(). (1) A,.f(z)a.
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.,5.7,K-{a},a(af(z) ,az,f(z)=A. ,,aK-{a}f(z)A).(1),a{zn},
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5.85.9A=A
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5.10A=A=0A, A
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5.9(()) af(z),A,A=A0,a{zn}f(zn)=A (n=1,2,).
- 5.2.4 Schwarz (Schwarz) f(z)|z|
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