# Search results

5. ### Higher Level Integration Marathon & Questions

I=\int_0^{2\pi} (\frac{e^{it}+e^{-it}}{2})^{2n}\, dt \\ \\ = 2^{-2n}\binom{2n}{n}\int_0^{2\pi}\, dt\\ \\=\frac{\pi}{2^{2n-1}}\binom{2n}{n}.\\ \\ $(all nonconstant trig monomials integrate to zero.)$
6. ### Higher Level Integration Marathon & Questions

Fair enough, seems a rather subjective matter...to me polylog and polygamma manipulations are okay, but I also have no qualms about using contour integration etc.
7. ### Higher Level Integration Marathon & Questions

Eh I wouldn't say that necessarily, I did the integral in a not particularly imaginative way...there could be a clever shortcut. To me it does seem like computing this integral is roughly the same mathematical "depth" as computing some particular values of the di/trilogarithm though. Anyway...
8. ### Higher Level Integration Marathon & Questions

^ That was good practice! I need to go out for dinner v soon, so will supply gory details later. In short, the answer can be expressed solely in terms of Apery's constant zeta(3). 1. IBP to essentially reduce the integral to log^2(1+x)/x. (The bulk of the difficulty of the originally posted...

Gg man, pretty well played. Shame about that pawn blunder.

Someone has joined, but just isn't moving lol.

Coming? Otherwise someone else join pls :).

https://lichess.org/dhv78LH8

Sweet, will host up in a sec. 15+10 or thereabouts seem decent? or would you prefer something else?

Cool, should be a decent game then. Free now?

Sure I'll be free later this arvo most likely for a few on lichess. How strong are you btw? Also theres some overlap between the part of the brain used in maths and chess respectively imo, but its hard to draw conclusions. The average mathematician who tries his hand at chess tends to do better...

Good bump. People hit me up for games, am really enjoying chess atm :).
17. ### BoS Maths Trials 2017

I think the Q16h solution is still not quite correct. Whilst it is true that x-k\alpha =< x for each x, we cannot simply bound the product of factors of this form by the product of the x's, as some of these terms will in general be negative. Another way of seeing this problem is that if we...
18. ### BoS Maths Trials 2017

What is the reasoning behind the second line of the estimate for |Q(k*alpha)| in the solution to Q16h) ? As written, that does not seem complete to me.
19. ### Inequalities

Defs try other methods first. It's extremely rare that an inequality will be easier / more natural to prove by contradiction than directly.
20. ### Same Sex Marriage Debate

What is this claim based on? And ANY heterosexual couples have the legal right to a marriage, and the benefits that come with. There are plenty of heterosexual couples that are in high likelihood going to be awful parents to any children they raise or do not want to have children at all, yet a...