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Results tagged with elementary-proofs
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user 5712
For questions related to 'elementary' proofs in a technical sense, which has nothing to do with the difficulty of the argument or result. A typical example would be 'elementary' proofs of the Prime Number Theorem, which avoid complex analysis. The tag is however not limited to this particular notion of 'elementary.'
10
votes
Different derivations of the value of $\prod_{0\leq j<k<n}(\eta^k-\eta^j)$
Your are asking about determinant of the Schur Matrix. So you can use original Schur's article or another classical expositions mentioned at Mathworld.
- 12.3k
7
votes
Accepted
Simplifying a double sum of inverses
We have
$$f(n+1)-f(n)=\frac1{n^2}+\frac2{n}\left(1+\frac 12+\ldots+\frac 1{n-1}\right)-\frac2{n+1}\left(1+\frac 12+\ldots+\frac 1{n}\right),$$ and $f(2)=0$. So
\begin{gather*}
f(m)=\sum_{n=2}^{m-1}(f( …
- 12.3k
11
votes
Accepted
Length of Hirzebruch continued fractions
Lets call expansions
$$\langle
x_1,\ldots,x_m\rangle:=\cfrac{1}{x_1-{\atop\ddots\,\displaystyle{-\cfrac{1}{x_m}}}}$$
(as in Perron's book) reduced regular continued fractions (RRCF).
Probably they are …
- 12.3k