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N is the set of natural nummbers anod C is the set of complex numbers, regian Nno=?ho, Mo tt, Hot+27 do the fetlowing Let Icc be a and ino EN} accordingty , A complex function series such as. defined'in region I, there is a number (wn) positive such that for each nE Nn and ZEI there is fn(z)|sWn, and if the E Wn Series is Convergent , then the Ž fn (z) sequence れ。 n=ho Complex function series is uniformly convergent . Prove it. Find two different bypes of Complex function series that satisfy the above theorem and show their correctness.

N is the set of natural nummbers anod C is the set of complex numbers, regian Nno=?ho, Mo tt, Hot+27 do the fetlowing Let Icc be a and ino EN} accordingty , A complex function series such as. defined'in region I, there is a number (wn) positive such that for each nE Nn and ZEI there is fn(z)|sWn, and if the E Wn Series is Convergent , then the Ž fn (z) sequence れ。 n=ho Complex function series is uniformly convergent . Prove it. Find two different bypes of Complex function series that satisfy the above theorem and show their correctness.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Nis the set of natural numbers and C isthe set of complex numbers, and Let Icc be a regian Nno=ho Ho tt, Hot2 , do the fottowing i no EN} accordingty @ A complex function series such as Ź fn (z) (wnt positive n. defined in region I , there isa number sequence such that for each ne N and ZEI there is fn(z)|s wn, and ifthe E Wn Series is Convergent, then the Ž fn (z) n=ho complex function series is unitormly convergent. it, Prove it. D Find two different bypes of complex function series that satisfy the above theorem and shaw their correctness.
Transcribed Image Text:Nis the set of natural numbers and C isthe set of complex numbers, and Let Icc be a regian Nno=ho Ho tt, Hot2 , do the fottowing i no EN} accordingty @ A complex function series such as Ź fn (z) (wnt positive n. defined in region I , there isa number sequence such that for each ne N and ZEI there is fn(z)|s wn, and ifthe E Wn Series is Convergent, then the Ž fn (z) n=ho complex function series is unitormly convergent. it, Prove it. D Find two different bypes of complex function series that satisfy the above theorem and shaw their correctness.
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