I have no idea what the dog is to be honest, I have never had any in my life and have had friends with mostly standard dogs e.g. Golden retriever, Huskie, Labrador, dalmatian
@Chris'ssis Hello Chris's, any interesting integral today
@IceBoy Those guys will close my questions immediately although I don't know if they (or a part of those that vote for closing) were really able to solve them ...
This is an integral coming from personal research, and very important to me, but it does not
seem
an easy job to do. If a solution is not possible then I'd be glad with a closed form only.
$$\int_{[0,1]^2} \frac{(1-x-y+x y+x \log(x)-x y\log(x)+y \log(y)- x y\log(y)+x y\log(x)\log(y))\log(1+x y)}...
I would naively suggest $t = 1+xy$ and it becomes a problem of identifying anti derivatives of expressions involving $log$ and $Li_2$ .. but Ilazy lol :P
@Alizter What does that imply about fields with many users? Are you saying that the fields(listed above) aren't accessible(without specialised training)?
Here I have a question I just received, and still trying to find a proper starting point
$$\int_0^1 \frac{(1-x+x\log(x))\operatorname{Li_3(x)}}{(x-1) x \log(x)} \ dx$$
What starting point would you propose?
@N3buchadnezzar: Thank you so very much :D Also, that paper you're searching for is as hard as nails to find. It is most likely that you will find the paper in Versailles, France inside of Serret's tomb. lol
@N3buchadnezzar: It's not discoverable online. Maybe some library or book has it. You can definitely get your hands on it if you track down some of his friends from École Polytechnique. (though, they're most likely dead as well)
@Committingtoachallenge I'm looking at your reading list and I'm seriously considering following in your footsteps. It's so difficult to stay motivated without any goals.
Wait, are there not communities on the internet whose sole purpose of existing is to digitize important scientific matter and bring it to the hands of the general public?
@Nick but it's not the same function, so that won't apply.....this is for my gf :) she hasn't learnt L hospital :) That is why :) so can't tell her this :)
@Nick I can teach :) but the problem is thsts not expected ...because it's her assignment, since she hasn't been taught that by profs...so they expect students to do without it...Atleast for now
Thanks to @David H's comment I got that
$$\int_0^1 \frac{(1-x+x\log(x))\operatorname{Li_3(x)}}{(x-1) x \log(x)} \ dx=\frac{5}{4}\zeta(4)-\gamma \zeta(3)+\zeta'(3)$$ that is proving to be numerically correct.
@BalarkaSen Over $\mathbb{C}\setminus \{0\}$, the Riemann surface is a cylinder, or a punctured plane. On one end of the cylinder, one glues $0$, on the other end $\infty$. If you leave off $\infty$, I don't see how you can get something that is a compact surface minus more than one point. But, all this geometric stuff isn't my forte, so I can't be sure that you're wrong.
@BalarkaSen: There is an easier way to evaluate the second guy ($\lim_{x\to 0}\frac{1 - \cos x}{x}$) using plain old trigonometry. We don't need no Taylor :D
can one of you explain how to convert an object in cartesian coordinates to cylindrical ones? I've having a lot of trouble and can't find good resources on it
my problem specifically is this: Use cylindrical coordinates to find the volume of the prism whose base is the triangle in the xy-plane given by y = 0, x = 1, and y = $\frac{7}{2} x$, and whose top is given by z = 8 - y