POWER SERIES.docx - POWER SERIES There are two types of series expansions that are important for working with complex functions power series The Laurent

POWER SERIES.docx - POWER SERIES There are two types of...

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POWER SERIES There are two types of series expansions that are important for working with complex functions. power series The Laurent Expansion First we will discuss of a power series with some fact about series of complex functions. Sequence and Series of Complex Number 1.Complex Sequence The basic definitions are as in calculus. An infinite sequence or, briefly, a sequence , is obtained by assigning to each positive integer n a number z n called a term of the sequence, and is written z 1 , z 2 ,……briefly…..z n We may also write z 0 , z 1 ……. Or z 2 , z 3 ……. or start with some other integer if convenient. We will also assume some familiarity with real sequences and series. As mention above z n is a complex number for each positive integer n. If we write z n =x n +iy n , then the complex sequence z n converges to L=c+id exactly when This reduces every complex sequence to a consideration of two real sequences 2. Complex Series Complex series are treated similarly in terms of their counterparts. Suppose
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