Book ChapterDOI
Functions of a Complex Variable
Jon H. Davis
- pp 279-343
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TLDR
In this paper, a theory of complex-valued functions of a complexvalued argument is presented, which contains some remarkably powerful results which are applicable to a variety of problems, such as the Fourier series expansion.Abstract:
In earlier chapters, complex-valued functions appeared in connection with Fourier series expansions. In this context, while the function assumes complex values, the argument of the function is real-valued. There is a highly developed theory of (complex-valued) functions of a complex-valued argument. This theory contains some remarkably powerful results which are applicable to a variety of problems.read more
Citations
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References
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Book
A treatise on the theory of Bessel functions
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Book
Theory of Functions of a Complex Variable
TL;DR: In this paper, the Laurent series is used for expanding functions in Taylor series, and the calculus of residues is used to expand functions in Laurent series volumes II, III, and IV.
Book
Complex Variables and Applications
TL;DR: In this paper, Cauchy-Goursat Theorem 2.1.1 was extended to include the point at infinity and the point of infinity at infinity in the definition of differentiability of analytical functions.