什么是holomorphic functions
时间: 2023-11-28 22:05:30 浏览: 37
Holomorphic functions are complex-valued functions that are differentiable at every point within a region of the complex plane. They are also sometimes referred to as analytic functions.
In other words, a function f(z) is holomorphic within a region if it has a derivative at every point within that region. The derivative of a holomorphic function is also a holomorphic function, and holomorphic functions have a number of interesting properties, such as the fact that the value of the function within a region is completely determined by its values on the boundary of that region, known as the Cauchy integral formula.
Holomorphic functions play an important role in complex analysis and have many practical applications in engineering, physics, and other fields. They are also closely related to other mathematical concepts, such as power series, which can be used to represent them in terms of convergent infinite series.
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