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visits member for 2 years, 6 months
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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.
Apr
15
comment Optimization issue, how to obtain the maximal value?
@user14002 Do you know about www.coursera.org ? If you search for the "Calculus One" course there is a whole video section about "Optimization" which will help you find your maximum.
Apr
14
comment Finding argument of a complex number
Since a complex number can be plotted on the plane, you can draw a line from the origin to the point and use $\tan$ to obtain the angle the line makes with the positive real axis.
Apr
14
comment Optimization issue, how to obtain the maximal value?
@user143002 I don't have time right now, but will take a look later unless someone else does. One tip: let $B=0$ and try to solve. Then let $B=1$ and try to solve, and so on. You may see a pattern arise !
Apr
14
comment Optimization issue, how to obtain the maximal value?
You could try to simplify first, e.g. since $N$ and $B$ are identified positive integers, then ${N+B\choose B}$ can be replaced by a constant, $\lambda$, say. You may also be able to simplify the sum in the denominator using the Binomial Theorem somehow.
Mar
26
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
@GerryMyerson - so we just take logs and apply the usual tools?
Mar
26
comment Why does this product diverge?
Ok, thanks all I think I've cleared this up now. Basically it all depends on what we mean by an infinite product. Using the standard "sequence of partial products" then we have divergence, but if we explicitly state @Sabyasachi's intention, $$\lim_{n\to\infty}\prod_{k=1}^{2n}a_n,$$ then we have convergence. Delicate!
Mar
26
comment Why does this product diverge?
This is where I misunderstand. The upper index in the product is always $2n$, so by definition the product is never defined with an upper index of $2n+1$. Maybe this is one of those "murky" $\infty$ areas since $\infty$ is not a natural number? ...
Mar
26
comment Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
When $p=1$, taking logarithms gives $\log p=0$ not $\log p=\infty$. Is that a typo?