Questions tagged [complex-analysis]
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Why is the Mean Value Theorem (of holomorphic functions) called "Gauss's"?
A handy special case of the Cauchy Integral Formula says that, if a complex function $f$ is analytic on and inside a circle of radius $r$ around $a$,
$$f(a) = \frac{1}{2\pi}\int_0^{2\pi} f(a +re^{it}) ...
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Where can I find Weierstrass's research notes?
I want to know the researth results of Weierstrass in 1841, where he proved some theories about Laurent series. Can you help me find it? I'd appreciate it if you can do me a favor!:)
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Translated articles of Fatou and Julia
Is there any English translation of the 1918-1920 Memoirs of Fatou and Julia on the iteration of rational functions?
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How were complex analysis methods, like the Joukowsky transform, used in early aircraft design?
The Joukowsky transform is a conformal mapping of a disk to an airfoil shape.
The wiki page says that "it was historically used to understand some principles of airfoil design".
That's kind ...
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Who first considered signed area?
Who first suggested that the area enclosed by a closed path and that enclosed by that path traversed in reverse could be regarded as equal in magnitude but opposite in sign?
Cauchy must have noticed ...
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Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved?
I asked this question on MSE and comments suggested I should ask it here
I am currently reading Baby Rudin as my second analysis book (after Introduction to Real Analysis by Robert G. Bartle and ...
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Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved? [duplicate]
I didn't know that can happen and since I already asked the question here I don't know what to do with this question should I delete it ?
I am currently reading Baby Rudin as my second analysis book (...
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To what extent were Riemann surfaces a precursor to algebraic geometry?
I read that Riemann started studying the so-called Riemann's surfaces in the second half of the 19th century, introducing tools like meromorphic functions and meromorphic 1-forms. The culmination of ...
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The history and origin of the Argument Principle ( or Cauchy's argument principle)
I am looking for a book that discusses The history and origin of the Argument Principle ( or Cauchy's argument principle) Thanks!
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Origin of the term "affixe"/"affix" in the geometric treatment of complex numbers
In current French mathematical tradition, when introducing complex numbers, it is common to hear about "complex plane of Argand-Cauchy".
What is particular in French treatment, it is the ...
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Who introduced the stream function?
I have found many different claimed answers to this question:
Wikipedia article on the stream function claims that Lagrange introduced it in 1781.
Darrigol's The Worlds of Flow says that D'Alambert ...
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Poisson integral formula
The term Poisson integral formula may refer to any of the related formulas for harmonic (or holomorphic) functions on a disk (or in a ball, half space, etc) in terms of their boundary values. This is ...
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History of the definition of complex derivative
Almost all of modern complex analysis (Cauchy residue theorem, analytic continuation, etc) depend on the definition of a complex derivative.
That definition requires the derivative at a point $z_0$ is ...
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What is the significance of Gauss-Weierstrass's derivation of "Al functions"?
In a fragment entitled "inversion of the elliptic integral of the first genus" (Gauss's werke, volume 8, p. 96-97), Gauss inverts the general elliptic integral of the first kind: he writes $\...
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Reference request for Gauss's original discovery of the special property of the $j$ function
In Interchapter VII of his biography of Gauss, W.K. Buhler describes Gauss's discovery of one of the important properties that characterize the $j$ invariant (Klein's absolute invariant; Gauss called ...
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