- #1
Silviu
- 624
- 11
Hello! Can someone explain to me in an intuitive way the difference between pointwise and uniform convergence of a series of complex functions ##f_n(z)##? Form what I understand, the difference is that when choosing an "N" such that for all ##n \ge N## something is less than ##\epsilon##, in the case of uniform convergence N can't depend on z but in the case of pointwise convergence it can. I saw an example for the function ##f_n(z)=z^n## which has uniform convergence if the domain is ##D_{[0,a]}## with ##a<1##, but has pointwise convergence for ##a=1##. I understand that the proofs involves different approaches and this is why they have different types of convergence, but in the end they converge to the same function ##f(z)=0##. So how is the uniform convergence stronger than the other one (I know that pointwise is implied by uniform but not the other way around, but this still doesn't really give me a clear understanding). Thank you!
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