Is there a reason why $\text{Arg}(z)$ behaves like a logarithm?

Find limit at 0 of cosine function with embedded sine

Closed form of $\frac{e^{-\frac{\pi}{5}}}{1+\frac{e^{-\pi}}{1+\frac{e^{-2\pi}}{1+\frac{e^{-3\pi}}{1+\ddots}}}}$

Irreducible representations of $SO(N)$

Basic question about real-analytic functions

summing this binomial series

If $f: \mathbb{N} \to \mathbb{N}$ and $\forall x \in \mathbb{N},\,(f \circ f )(x) = x^{4}$, is $f$ polynomial?

Need help with this proof via induction

If $X\subset L^1$ is a closed vector space and $X\subset \bigcup_{1<p\leq\infty} L^p$ then $X\subset L^q$ for some $q>1$.

Three externally touching circles have their centers on the same line and have radii $a$,$b$ and $c$ (where $a<b<c$).Prove that $b^2=ac$.

Can a triangle ABC be made if $\frac{\cos A}{2}=\frac{\cos B}{3}=\frac{\cos C}{7}$

Given a self-map $h$ of a (closed?) manifold, is there a vector field $\xi$ with flow $\Phi_t$ such that $h = \Phi_1$?

The relation between uniform integrability and dominated convergence theorem in the case of counting measure

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