# Tagged Questions

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### How and why did Weierstrass $\wp$ get its special symbol?

I kind of always hated drawing the Weierstrass $\wp$ symbol by hand, and it struck me as odd how and why it achieved its special status in the first place. After all, there are tons of other important ...
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### Uses of Jacobian of a map on $\mathbb{R}^n$.

For a map $f:\mathbb{R}^n\to\mathbb{R}^n$, Jacobian matrix of $f$ is defined as \begin{bmatrix} \frac{\partial f_1}{x_1}& \frac{\partial f_1}{\partial x_2}& \ldots \frac{\partial ...
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### Who proved Fundamental Theorem of algebra using Liouville's theorem?

One of the most famous proofs of the Fundamental Theorem of Algebra involves Liouville's theorom stating that a bounded entire function in constant. Who first came up to the idea of deriving FToA ...
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### sin(x) infinite product formula: how did Euler prove it?

I know that $\sin(x)$ can be expressed as an infinite product, and I've seen proofs of it (e.g. Infinite product of sine function). I found How was Euler able to create an infinite product for sinc by ...
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### Weierstrass and Borel summation

In the Wikipedia article on Borel summation, there is the following quote attributed to Gösta Mittag-Leffler: Borel, then an unknown young man, discovered that his summation method gave the ...
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### Square root principle value convention

Why is the principal square root of a complex number defined as $\sqrt z = \sqrt r e^{-i \varphi / 2}$ for $\varphi \in (-\pi, \pi]$ ? Wouldn't it be more natural to let $\varphi \in [0, 2\pi)$ as it ...
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### Who is responsible for the analytical/topological proof of FTA?

The fundamental theorem of algebra asserts: Theorem Let $P$ be a polynomial of degree $\geq 1$ in $\Bbb C$. Then there exists a $z_1\in\Bbb C$ such that $P(z_1)=0$. The proof sketch goes as ...
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### When was the significance of $i$ first noticed?

Complex analysis is an entire field of mathematics that focuses on the use of the complex constant $i$. When was the significance of $i$, an imaginary number, first noticed? If I did not know some ...
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### “fluent” functions

In an old mathematics book (Ritt, 1948, p.5) I have come across the notion of "monogenic analytic" and "fluent" functions. These are complex valued functions. Has anyone heard of these terms before? ...
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### Lie and Weierstrass' visualization of complex functions

I am reading Whittaker and Watson's A Course of Modern Analysis. In the third chapter where they discuss different ways to visualize functions that map the complex plane to the complex plane, they ...