This concept develops the theory of sequences and series of complex-valued functions, distinguishing pointwise convergence from the stronger notion of uniform convergence, and establishes that uniform convergence (unlike pointwise convergence) preserves continuity, permits interchange of limits with integration, and preserves analyticity. It belongs to complex analysis, building on real-series convergence results (absolute convergence implies convergence, via comparison with real/imaginary parts) and connecting function-sequence convergence to core complex-analytic tools such as Cauchy's theorem, Morera's theorem, and the Cauchy integral formula.
This concept develops the theory of sequences and series of complex-valued functions, distinguishing pointwise convergence from the stronger notion of uniform convergence, and establishes that unifor…