Transcription of 5. Taylor and Laurent series Complex sequences and series
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5. Taylor and Laurent series Complex sequences and series
And Laurent seriesComplex sequences and seriesAn infinite sequence of Complex numbers, denoted by{zn}, can beconsidered as a function defined on a set of positive integersintothe unextended Complex plane. For example, we takezn=n+ 12nso that the Complex sequence is{zn}= 1 +i2,2 +i22,3 +i23, .Convergence of Complex sequencesGiven a Complex sequence {zn}, if for each positive quantity , thereexists a positive integerNsuch that|zn z|< whenevern > N,then the sequence is said toconvergeto the limtz. We writelimn zn= In general, the choice ofNdepends on.
5. Taylor and Laurent series Complex sequences and series An infinite sequence of complex numbers, denoted by {zn}, can be considered as a function defined on a set of positive integers into the unextended complex plane. For example, we take zn= n+ 1 2n so that the complex sequence is {zn} = ˆ1 + i 2, 2 + i 22, 3 + i 23 ...
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