From sequences of numbers, we turn to sequences of functions. Then our concern is with both the form of convergence and the behavior of the limit function. Convergence, determined at each point in a set, need not require the limit function to retain any of the properties common to each function in the sequence. But if a certain “rapport” exists between the sequence of functions and the set, then the limit function will be forced to confirm to definite standards established by the sequence. This stronger type of convergence, in which the set takes precedence over its points, is called uniform convergence.


Power Series Taylor Series Limit Function Uniform Convergence Complex Sequence 
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© Birkhäuser Boston 2006

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