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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.'
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
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