complex analysis
10 videos • 187 views • by msc mathematics
1
if ∑ an converges absolutely then ∑ an converges
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2
2.Σan(z-a)^n & 1/R=lim sup |an|^(1/n),(a)|z-a|‹R cnvrgs absltly (b)|z-a|›R unbndd & dvrgs (c)|z|≤r
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3
power series ∑ (an+bn) (z-a)^n and ∑ cn(z-a)^n have radius of convergence ≥r.
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4
If f: G→C is differentiable at a point a in G then f is continuous at a
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5
g•f is analytic on G and (gof)'(z)=g'(f(z))f'(z)
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6
f(z) =∑ an(z-a)^n have R ›0 (a) k ≥ 1 ; ∑ n(n-1)... (n - k + 1) an(z - a) ^(n-k) has R
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7
let f(z)=Σ an(z-a)^n|Σn(n-1)...(n-k+1)an(z-a)^(n-k) is R|f is infinitely diff on B(a,R)|an=f^n(a)/n!
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8
If G is open and connected and f:G→C is differentiable with f'(z) = 0 for all z in G,f is constant.
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9
G⊂C is open&connected, totality of branches of log z = functions f(z)+2πki, k ∈ Z.
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10
f is differentiable and f'(z) = 1/(g'(f(z)))
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