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 Yearling
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Jul
7
comment Computing the value of logarithmic series: $Q(s,n) = \ln(1)^s + \ln(2)^s + \ln(3)^s + \cdots+ \ln(n)^s $
yes it does approach zero because if you calculate the error term or Euler-Maclaurin, you will see it is bounded by the first derivative (ie $s(\log(n))^{s-1}/n$).
Jul
7
comment Computing the value of logarithmic series: $Q(s,n) = \ln(1)^s + \ln(2)^s + \ln(3)^s + \cdots+ \ln(n)^s $
You should expand your answer. Using just the first 3 terms of the Euler-Macclaurin formula, you can show that the error is less than $\frac{s}{12n}(\log(n))^{s-1}$ for $s\gt 1$. Unfortunately the error bound doesn't start going down until $n \gt e^{s-1}$.
May
22
answered Question about a proof that $\mathbb{Q}$ is dense in $\mathbb{R}$
May
21
comment How to calculate this multi-integral?
The sign is wrong. The last integral should be +1/2 sin(z).
May
4
comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$
@math110, it is the same. You only need to show $n! > 2e^{-\lambda n} \int^{\lambda n}_0 (\lambda n -t)^n e^t dt$ which follows basically what you have already.
May
4
comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$
@math110, I meant replace your argument of $x=n$ with $x=\lambda n$ and you will arrive at the same conclusion you have for $x=n$.
May
4
comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$
I think you can do this by letting $x := \lambda n$ where $0 \lt \lambda \le 1$. All your inequalities will remain true.
Jan
16
comment Lost on algebra notation
@Clayton, I think that's an exaggeration. Most undergrad number theory books don't require much algebra prerequisites if any (eg, old books like Landau and Hardy/Wright).
Dec
24
comment Proving that $\left(1+\frac{z_{1}}{z_{2}}\right)\left(1+\frac{z_{2}}{z_{3}}\right)…\left(1+\frac{z_{n}}{z_{1}}\right)\in\mathbb R$
should be 2\cos(t_i-t_j)e^(i(t_i-t_j))?
Sep
19
comment Limit of an integral containing a product
Are the integral limits 1 to infinity and do you mean N approaches infinity instead of of x?
Mar
30
comment If a rational number has a finite decimal representation, then it has a finite representation in base $b$ for any $b>1?$
Not true. 0.1 base 10 = 0.00011001100110011.... in base 2.
Mar
28
answered Real Analysis Book Choice
Mar
24
comment How can I use Cauchy integral formula for this integral $g(z)=\int_{C}\frac{s^2+s+1}{s-z}ds$?
Also you should remember if f(z)/(z-z_0) is analytic within and on C, then the integral is 0.
Mar
12
comment Chernoff bounds - basic results
One question: did you check the Wikipedia article on Chernoff Bound?
Mar
1
comment Statistics resources with examples for a C.S. student
He wants statistics resources not probability.
Feb
27
awarded  Yearling
Feb
19
answered Mathematical function for the powers
Jan
28
comment Conditional expectation $E[X\mid\max(X,Y)]$ for $X$ and $Y$ independent and normal
@Didier Piau, thanks for the clarification! For some reason I had always thought $;$ or $|$ meant the same thing; similar to $:$ and $|$ for describing sets.
Jan
28
comment Conditional expectation $E[X\mid\max(X,Y)]$ for $X$ and $Y$ independent and normal
@Didier Piau, I don't understand why the numerator isn't $zf_X(z)F_Y(z) + \mathbb{E}(X|X \le z)f_Y(z)F_X(z)$.
Jan
22
comment Real life applications of Topology
Knowledge of topology is often crucial for passing your PhD qualifying exams in math. You do want your PhD, don't you?