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Aug
26
revised Cramer, $P(S_n\geqslant na)\sim e^{-n I(a)}$
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Aug
26
answered Cramer, $P(S_n\geqslant na)\sim e^{-n I(a)}$
Aug
26
comment Cramer, $P(S_n\geqslant na)\sim e^{-n I(a)}$
You mean $$\lim_{n \to \infty} \dfrac{1}{n} \ln P(S_n \ge n x) = -I(x)$$
Aug
26
comment Conditions for convergence of derivatives from pointwise convergence
Uniform convergence on compact sets would work if these were analytic functions on $\mathbb C$.
Aug
26
revised Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
added 11 characters in body
Aug
26
answered Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
Aug
26
comment Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
See OEIS sequence A174094 (oeis.org/A174094) which has $f(n)$ for $n = 1..46$. The logarithmic scatterplot makes it plausible that $f(n) \sim a \exp(b n)$ for some $a,b$ with $b > 0$, but very implausible that $f(n) = o(n)$.
Aug
25
comment Deducing absolute convergence in particular cases from invariance under rearrangements
Maybe not strictly relevant here, but in infinite-dimensional Banach spaces unconditional convergence does not imply absolute convergence. So if you look at the literature on unconditional convergence in Banach spaces you might see examples of series being proved unconditionally convergent without the benefit of absolute convergence.
Aug
25
answered Guessing particular solution for a recurrence relation with multiple quasi-polynomials on the right side
Aug
25
comment Given sequence of harmonic functions converges uniformly on compact subsets
The real part is greater than $0$. All you need for Montel is that they omit two values (e.g. $0$ and $-1$). If the question is correct, the real parts all converge to $0$. We don't know what the imaginary parts do, but we can always add an imaginary constant so the imaginary part of $f_n(z_0)$ is, say, $0$.
Aug
25
revised Is there any good software that solves equations of permutation group elements?
added 691 characters in body
Aug
25
answered Is there any good software that solves equations of permutation group elements?
Aug
25
answered Given sequence of harmonic functions converges uniformly on compact subsets
Aug
25
answered Various forms of the Confluent Heun Equation
Aug
25
revised Various forms of the Confluent Heun Equation
Third term in the Confluent Heun equation needed a y
Aug
25
comment Abelian-by-(finite abelian)
What do you mean by that?
Aug
25
revised exercise Question-29 from contemporary abstract algebra
More appropriate tags
Aug
25
answered exercise Question-29 from contemporary abstract algebra
Aug
25
comment Definition in Operator Theory
From en.wikipedia.org/wiki/Functional_calculus : In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. ... The idea of a functional calculus is to create a principled approach to this kind of overloading of the notation.
Aug
25
answered $f(x)$ be the characteristic polynomial of a matrix $A \in M_n(\mathbb R)$ ; then is it true that $f(1)=1+\operatorname{trace}(A)+O(\|A\|^2)$?