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.

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