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Engineering Mathematics, Volume III by E. Keshava Reddy, E. Rukmangadachari

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5

Complex Power Series

5.1 Introduction

In calculus, we have studied 1Taylor’s and 2Maclaurin’s power series expansions in the forms ∑an(za)n and ∑anzn in respect of elementary functions. We now extend these to functions of complex variables. Further, we study here another type of expansion known as 3Laurent’s series expansion which involves both positive as well as negative powers of (za). These expansions help us in the study of the properties of functions, in numerical computations and in the evaluation of certain real integrals.

5.2 Sequences and Series

Let S be a set of complex numbers. We can form a complex sequence by choosing from S a first number u1, a second number u2, and so on. Here u1, u2,… un,… are called the first, the ...

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