Functions of a Complex Variable
Functions of a Complex Variable
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DOI：
10.1017/cbo9780511755781.007
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发表时间：
1964
期刊：
影响因子：
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通讯作者：
E. Saff;A. D. Snider;Prentice Hall
中科院分区：
文献类型：
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作者：
E. Saff;A. D. Snider;Prentice Hall
在本章中，我们将研究复变函数。复平面上最有趣的函数是那些全纯函数。最重要的全纯函数是指数函数和对数函数。全纯性是可微性的复杂类比，但由于各种原因，我们将详细研究，全纯函数比可微函数更具限制性。本章的重点将是幂级数和具有局部幂级数展开的函数，即，解析函数原因有二：
In this chapter, we will study functions of a complex variables. The most interesting functions on the complex plane are those that are holomorphic. The most important holomorphic functions are the exponential and the logarithm function. Holomorphicity is the complex analogue of differentiability, but for various reasons, which we shall study in great detail, a function being holomorphic is far more restrictive than the function being differentiable. The focal point of this chapter will be power series and functions that have local power series expansions, i.e., analytic functions. The reason for this is two-fold: