Here is a question that naturally arose in the study of some specific integrals. I'm curious if for such integrals are known nice real analysis tools for calculating them (including here all possible sources
in literature that are publicaly available). At some point I'll add my solution.
It's a...
Here is a question that naturally arose in the study of some specific integrals. I'm curious if for such integrals are known nice real analysis tools for calculating them (including here all possible sources
in literature that are publicaly available). At some point I'll add my solution.
It's a...
It is a generalization of this question. I am looking for a similar derivation as in here.
Can we prove that $(1+p/n)^n$ is a Cauchy sequence for any $p \in [a, b]$ by showing that
$$ \Bigg| \left( 1 + \frac{p}{n}\right)^n - \left( 1 + \frac{p}{m}\right)^m \Bigg| \leq f(n)$$
where $f(n)$ is so...
I have heard the term "coalgebras" several times in functional programming and PLT circles, especially when the discussion is about objects, comonads, lenses, and such. Googling this term gives pages that give mathematical description of these structures which is pretty much incomprehensible to m...
I want to prove the following lemma:
$t^n-1$ divides $t^m-1$ in $F[t, t^{-1}$ if and only if $n$ divides $m$ in $\mathbb{Z}$.
I have done the following:
$\Leftarrow $ :
$n\mid m \Rightarrow n=km, k \in \mathbb{Z}$
$t^n-1=t^{km}-1=(t^m)^k-1=(t^m-1)(t^{m(k-1)}+\dots +1)$
So, $t^n-1\mid t...
Here is a question that naturally arose in the study of some specific integrals. I'm curious if for such integrals are known nice real analysis tools for calculating them (including here all possible sources
in literature that are publicaly available). At some point I'll add my real analysis so...
I've been looking at proofs of this equation:
$$\displaystyle \frac {\sin \pi x} {\pi x} = \displaystyle \prod_{k \mathop = 1}^\infty \left({1 - \frac{x^2}{k^2} }\right)$$
All the proofs seem to rely on complex analysis and fourier series. Is there a (more) elementary proof?
