You get a bonus - 1 coin for daily activity. Now you have 1 coin

Comprehensive function

Lecture



The term complex function can refer to two types of functions:

Content

  • 1 Complex function
  • 2 Function integrated variable
  • 3 See also
  • 4 Literature

Complex function [edit]

The complex-valued function is a function of a real variable having complex values:

  Comprehensive function .

Such a function can be represented as

  Comprehensive function ,

Where   Comprehensive function and   Comprehensive function - real functions. Function   Comprehensive function called the real part of the function   Comprehensive function , but   Comprehensive function - its imaginary part .

Complex Variable Function [edit]

This concept is a generalization of the previous version:

  Comprehensive function .

Such functions are handled by a separate area of ​​mathematical analysis - the theory of functions of a complex variable, or complex analysis.

The function can also be represented as

  Comprehensive function ,

however, there is a deeper connection between   Comprehensive function and   Comprehensive function . For example, in order to function   Comprehensive function was differentiable, the Cauchy – Riemann conditions must be satisfied:

  Comprehensive function ;
  Comprehensive function .

Examples of analytic functions of a complex variable are: a power function, an exponent, a gamma function, a Riemann zeta function and many others, as well as their inverse functions and any combinations thereof. However, the real part of the complex number   Comprehensive function , complex part   Comprehensive function complex conjugation   Comprehensive function module   Comprehensive function and argument   Comprehensive function analytical functions of a complex variable are not, since they do not satisfy the Cauchy – Riemann conditions.

created: 2014-10-25
updated: 2021-03-13
132515



Rating 9 of 10. count vote: 2
Are you satisfied?:



Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Comprehensive analysis and operational calculus

Terms: Comprehensive analysis and operational calculus