meta user
network profile
| bio | website | sites.google.com/site/… |
|---|---|---|
| location | Canada | |
| age | ||
| visits | member for | 2 years, 4 months |
| seen | 7 hours ago | |
| stats | profile views | 5,957 |
I an interested in Number Theory, Analysis and Additive Combinatorics. My papers can be found here, or you can visit my website for more information.
|
1d |
awarded | Nice Answer |
|
May 18 |
awarded | Constituent |
|
May 15 |
revised |
Proving two sequences identical edited body |
|
May 14 |
awarded | Good Question |
|
May 13 |
comment |
Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$ +1, Very nice solution. |
|
May 13 |
comment |
Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$ It's not clear how to proceed from $$\int_{0}^{\infty}\log u\frac{\sinh(u)}{\cosh(u)^{2}}du,$$ although it is a rather nice form. |
|
May 13 |
comment |
Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$ Here are some equivalent forms: Since $\text{sech}^{-1}(x)=\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^{2}}-1}\right),$ we are trying to evaluate $$\int_{0}^{1}\log\left(\text{sech}^{-1}(x)\right)dx.$$ Let $u=\text{sech}^{-1}x$ so that $x=\text{sech}(u)=\frac{1}{\cosh(u)}.$ Then $dx=d(\frac{1}{\cosh(u)})$ , and we are looking at $$-\int_{0}^{\infty}\log ud\left(\frac{1}{\cosh(u)}\right)$$ which equals $$\int_{0}^{\infty}\log u\frac{\sinh(u)}{\cosh(u)^{2}}du.$$ Using integration by parts, this becomes $$\lim_{a\rightarrow0}\left(\log a+\int_{a}^{\infty}\frac{\text{sech}(x)}{u}du\right).$$ |
|
May 13 |
comment |
How many $p$-adic numbers are there? @PatrickDaSilva: You need to check that the map is well defined. It also gives two surjections, not two injections. |
|
May 7 |
awarded | Informed |
|
May 6 |
comment |
Reflecting a golfball off a wall to a hole and compensating for the balls radius I am deleting the comments regarding the inappropriate username on this thread. The original username, and description, were not appropriate at all, and have been changed to something less offensive. They have been recorded in a previous deleted comment. |
|
May 6 |
awarded | Caucus |
|
May 6 |
revised |
To estimate $\sum_{m=1}^n \Big(d\big(m^2\big)\Big)^2$ added 125 characters in body |
|
May 6 |
answered | To estimate $\sum_{m=1}^n \Big(d\big(m^2\big)\Big)^2$ |
|
May 6 |
revised |
To estimate $\sum_{m=1}^n \Big(d\big(m^2\big)\Big)^2$ added 104 characters in body |
|
May 6 |
awarded | Announcer |
|
May 5 |
answered | Two questions re: $\sum_{n=1}^{\infty}n^{-p_{n}}$ |
|
May 5 |
answered | To estimate $\sum_{m=1}^n \Big(d\big(m^2\big)\Big)^2$ |
|
May 5 |
revised |
Divisor summatory function for squares edited tags |
|
May 5 |
revised |
analytic number theory, troubling bound on sum of $\varphi(n)$ added 271 characters in body |
|
May 5 |
revised |
analytic number theory, troubling bound on sum of $\varphi(n)$ deleted 23 characters in body |
