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4h
comment Lebesgue-Stieltjes: Computation
Without measure? Well, $\int_{-\infty}^\infty\eta(\lambda)\;\mathrm{d}\mu(\lambda)$ is a Riemann-Stieltjes integral, for example if $\eta$ is continuous.
9h
comment how to prove that $\lim\limits_{n\to\infty} \left( 1-\frac{1}{n} \right)^n = \frac{1}{e}$
Can you show the product $(1+1/n)^n \cdot (1-1/n)^n$ goes to $1$?
1d
answered double summations
1d
comment E-olymp: Cake. Giving Wrong Answer
Should e-olymp participants figure it out themselves, instead of asking us?
1d
answered Practical use for negative $dt.$
2d
comment Is integration of $x\operatorname{cosec}(x)$ defined?
Of course it is defined. But it is not an "elementary function".
2d
comment Eliminating rule of existential quantifier
First you say to do it "intuitively", which Clive's answer does. Then you say "But" and object to that.
Jul
1
comment Hints on solving $y''-\frac{x}{x-1}y'+\frac{1}{x-1}y=0$
Laplace has formulas for multiplying by the independent variable. They involve derivatives, but sometimes the new differential equation is easier than the original one.
Jul
1
comment Gamma function still hard for me
It seems your evaluation involves $(x+1)!$ where $x$ may not be an integer. That is where the gamma function is hiding.
Jun
30
comment Solve integrals using residue theorem?
If $z = e^{i\theta}$, then $f(z)dz = d\theta/(2+\cos\theta)$, maybe with a factor $i$ in there.
Jun
30
comment $L^{\infty}$ norm
Another way to sort out the question would be to find a simple case where your two candidates are different, and do the computation in that case. Say $n=2$ and the functions are constants.
Jun
30
comment Is this operator $A = \pmatrix{1&1\\0&1}$ self-adjoint?
I think it is safe to say that "self-adjoint" with no mention of a quadratic form means the usual quadratic form. And when we ask something about an "operator" but it is shown as a matrix, we assume it is asked about the linear transformation associated to that matrix in the usual way. And when it is not specified what field the entries are in, we assume the reals. And so on.
Jun
30
comment If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?
"Symmetry suggests that..." But of course you need more computation, as you have given. Note that also "symmetry suggests that" the minimum occurs when $u=v=w=x$.
Jun
29
comment Why is $\sum_{k=1}^{\infty}\mathbb{E}[\mathbb{1}(T=k)]=\sum_{k=0}^{\infty} k \mathbb{P}[T=k]$
user should reveal the secret source of this misinformation!
Jun
29
comment Not understanding the results of standard deviation
My guess: A1 is not a single measurement; but instead A1 was done by making lots of measurements (a "random sample"), and then these measurements were used to estimate that 15.4 was the mean and 1.91 was the standard deviation for A1.
Jun
28
comment Universal instantiation another question why couldn't?
I think you misunderstand "universal instantiation". For that, you need one $\forall$ applying to the whole thing.
Jun
27
comment Why is this not a valid proof?
How do you know that $A$ has an inverse? Once you do, then of course $B$ is it. But the problem is to start with $AB=I$, not knowing that $A$ has an inverse, and conclude $BA=I$. And from this it will follow that $B$ is the inverse of $A$.
Jun
27
comment When trying to learn analysis from bottom up, what numbers should I first construct?
When you do all these constructions, finally arriving at $\mathbb R$, do not fool yourself into thinking this is analysis. That only begins after you have $\mathbb R$ and its basic properties.
Jun
27
comment Long polynomial expansion with 34 roots
Perhaps the answer is $m+n=482$.
Jun
27
comment Convergence of $\int _{-\infty}^{+\infty}\sin(cx)dx$
Of course $$\mathrm{pv} \int_{-\infty}^\infty x^{2015}\,dx = 0$$ also. But perhaps a mathematician would say: so what?