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App development & Mathematics. Research Associate.


13h
comment Irrational number “test”?
@ Erick thank you very much for your answer. I had an inkling my thoughts might be "on the right track", but clearly "hadn't got it quite right" !
13h
comment Irrational number “test”?
@ Erick wow - I see that now: while $$\lim_{n\to\infty}\frac{u_n}{v_n} = \lim_{n\to\infty}\frac{n}{n+1}=1,$$ we have $$\lim_{n\to\infty}(n+1)\times 1-n=\lim_{n\to\infty} 1 = 1\neq 0.$$
17h
comment Basic graphing - plot v = 10i +4
You're probably getting confused by a use of different variable names. You are probably familiar with $x$ and $y$ ? Just replace $v$ with $x$ and $i$ with $y$ to get $x=10y+4$, or rearranging $y=(x-4)/10=x/10-2/5.$ Since this is the equation of a line, let $x=0$ to get a $y$ value, then let $y=0$ to get an $x$ value. Plot these two coordinates and join them to get your line.
20h
comment Irrational number “test”?
@ Erick but isn't this just the same as my original question, since $$\lim_{n\to\infty}v_n a-u_n=0 \iff \lim_{n\to\infty}a=\lim_{n\to\infty}\frac{u_n}{v_n}\iff a=\lim_{n\to\infty}\frac{u_n}{v_n},$$ and $u_n,v_n\to\infty$ as $n\to\infty$, $(u_n,v_n)=1$ ?
Aug
15
comment Irrational number “test”?
Thanks Erick. Do you have a reference for this or a resource for further details? I'd like to study more.
Aug
15
comment Irrational number “test”?
@Erick yes you're right. I've updated the question.
Aug
14
comment Evaluation of $\int_0^\infty \frac{(x^2+y^2)^{-s/2}}{e^{2\pi y}-1}\cos(s \arctan(y/x))dy$
@ OlivierOloa thank you that's very helpful.
Aug
12
comment Evaluation of $\int_0^\infty \frac{(x^2+y^2)^{-s/2}}{e^{2\pi y}-1}\cos(s \arctan(y/x))dy$
Why does the first part "give a divergent integral" ? I know the integrand behaves like $1/(2\pi y x^2)$ near $y=0$ which tends to $\infty$ as $y\to 0$, but how can we be sure that the integral of the integrand is not defined; c.f. $\int_0^1 x^{-1/2}dx = 2<+\infty$.
Jul
24
comment Computing a very messy contour integral
$z=0$ is not inside the contour.
Jul
21
comment How to solve the equations system?
You could try substituting (1) into (3) and then (3) into (2). Then solve for $y$. Then use your result for $y$ to obtain the remaining unknowns.
Jul
10
comment When is a limit of products not a product of limits?
yes I noticed this on your blog also.
Jul
10
comment When is a limit of products not a product of limits?
Thank you for the insight - very clear and helpful.
Jul
9
comment When is a limit of products not a product of limits?
Sorry @boywholived, I made a typo in my question. Amended.
Jul
9
comment When is a limit of products not a product of limits?
Yes you are right. I've edited the post.
Jul
9
comment Gamma function whose argument is a reciprocal power with integer base and exponent
@barakmanos sorry for the confusion. I meant that the argument is the reciprocal of an integer base and exponent.
May
13
comment Choosing referees for peer review
@Rahul I found similar questions on here (e.g. math.stackexchange.com/questions/294863/…), so thought it should be ok, but yes.
May
8
comment Properties of power series and their analytic continuation
@Daniel Properties such as $f(-z)=f(z)$ or functional equation type properties relating $f(z)$ and $f(1-z)$.
May
6
comment Integration method for $\int_0^\infty\frac{x}{(e^x-1)(x^2+(2\pi)^2)^2}dx=\frac{1}{96} - \frac{3}{32\pi^2}.$
that's great, thanks.
Apr
23
comment Standard notation for the indicator function of the odd integers
I think I'll use $\chi_{2\mathbb{Z}+1}(x)$ then. Thanks.
Apr
21
comment Evaluate $\int_a^s\frac{(t-s)^n}{t(t-z)^{n+1}}dt.$
@Claude - it's $s$; I've corrected the title.