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12:44 AM
@Starfall @amWhy @BrevanEllefsen Good thing I don't care about what you guys care about what other people do to other people who care about things in different ways relating to other people about...
2 hours ago, by Brevan Ellefsen
Last night I had a dream where I needed to find all the poles of $\frac{x^n}{1-x^s}$ so that I could calculate $\int_0^x \frac{t^n}{1-t^s} dt$. I doubt this approach would work in the slightest, but I wonder why I dreamed it.
@BrevanEllefsen I've probably been teaching you too much complex analysis
Indeed, that approach does actually work if you were trying to solving the following integral: $$P.V.\int_0^{+\infty}\frac{x^n}{1-x^s}~dx$$
 
@SimplyBeautifulArt =D
 
Where we work around the pole at $x=1$ the a principal value type limit
@amWhy :D
@theideasmith Hello and welcome to my realm!
@BrevanEllefsen If you wish, we can continue this conversation in my integral chat room
Hm, interesting... what kinds of topics in mathematics do you do @theideasmith ?
 
1:02 AM
@SimplyBeautifulArt I'm familiar with the solution when the limits are $0$ and $\infty$, but in my dream the upper limit was variable, I.E.$x$
 
That sounds horrible XD
 
@SimplyBeautifulArt was that comment directed at me?
 
Yes @BrevanEllefsen
:D
 
@SimplyBeautifulArt Haha. I would hardly say that it's you who has gotten me into complex analysis either, though I liked the humor XD I'm read through pieces of a couple PDFs and I should have a textbook coming on March 7th
@SimplyBeautifulArt is there a known solution for variable upper index?
Probably as a hypergeometric
But anything simpler than that?
 
Well, with the right substitution, geometric series, etc. it looks like it simplifies
 
1:15 AM
@SimplyBeautifulArt hmm
@SimplyBeautifulArt I'm making that the next thing I want to see solved in life
 
Mhm...
Oh, really?
Assuming that $x<1$, we have the following:
$$\int_0^x\frac{t^n}{1-t^s}~dt=\int_0^x\sum_{k=n}^\infty t^k~dt=\sum_{k=n}^\infty\frac{x^{k+1}}{k+1}$$
 
OK. So we have something that looks like the arctangent series
 
Lol, well it looks like it
Didn't say it is ir
 
I meant I made a mistake
 
1:22 AM
I'm trying to read unrendered MathJax on my phone, so don't look to me XD
 
$$\int_0^x\frac{t^n}{1-t^s}~dt=\int_0^x\sum_{k=0}^\infty t^{sk+n}~dt=\sum_{k=0}^\infty\frac{x^{sk+n+1}}{sk+n+1}$$
 
OK. What now. That does look better, reminds a little bit of Digamma function.
 
Nope. The Lerch Transcendent is better suited here
 
Oh yeah, you're right
I thought about that
But misread the mathjax XD
I need a phone rendering script :P
Hmmm
 
1:28 AM
Well, OK then. Any idea if it simplifies more than that? I'm dubious, but would be pleasantly surprised
 
That depends on the Lerch Transcendent ;-)
I doubt it of course.
 
Sure, but I'm curious
I'll make sure Mathematica doesn't simplify the Lerch Transcendent any more
 
sigh
it doesn't
 
1:31 AM
I finally grabbed a computer with MathJAx
which made this a whole lot easier XD
 
2:11 AM
0
Q: Interesting examples of differentiation under the integral sign?

Simply Beautiful ArtI was recently looking through integration techniques when I came upon differentiation under the integral sign (DUIS). It seems to be pretty powerful, for example: $$f(t)=\int_0^1\frac{x^t-1}{\ln(x)}\ dx\implies f'(t)=\int_0^1x^t\ dx=\frac1{t+1}\\\implies f(t)=C+\ln(t+1)\\f(0)=0\implies C=0\\\i...

 
 
5 hours later…
7:36 AM
@SimplyBeautifulArt
I answered a question similar to tht
Without DUIS
And, as I don't answer calculus questions,
1
A: Evaluating $\int_0^1 \frac{x^3-1}{\ln x}dx$

S.C.B.Note that substituting $x=e^{-t}$, your integral becomes $$\int_0^1 \frac{x^3-1}{\ln x}\mathrm{d}x=\int_{0}^{\infty} \frac{e^{-t}-e^{-4t}}{t} \mathrm{d} t$$ As $\ln x =-t$. Now use Frullani's Integral to get that $$\int_{0}^{\infty} \frac{e^{-t}-e^{-4t}}{t} \mathrm{d} t=\ln 4$$ As corroborated...

Is this right?
Traffic is really slow today.
 
 
2 hours later…
9:32 AM
@S.C.B. it's fine
@SimplyBeautifulArt i don't think that's a good thing at all
 
 
2 hours later…
12:01 PM
@S.C.B. looks good
@Starfall meh, whatever XD
 
 
1 hour later…
1:19 PM
@SimplyBeautifulArt Why was your answer the one accepted?
:(
Oh well.
 
@S.C.B. :-/
Because it looks cool?
 
Frullani is cool.
 
Mhm
@S.C.B. we can evaluate $$\int_0^\infty \frac{\sin(x)}x\ dx$$ using Frullani
 
 
1 hour later…
2:28 PM
@SimplyBeautifulArt How?
 
2:40 PM
@S.C.B. complex definition of sine
 
@SimplyBeautifulArt Is that contest still running?
 
Oh, good point.
@wythagoras Technically, it has ended, but @SimplyBeautifulArt has said that he is willing to accept more numbers.
 
3:25 PM
@SimplyBeautifulArt How can you do this integral?
$$\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}dx=\dfrac{\pi e}{4!}$$
Hello @Starfall.
 
hi
 
What brings you here?
 
nothing in particular
 
I haven't seen you on Quora lately.
 
as in, i haven't posted anything?
answering questions on quora is a tiring pastime
 
3:28 PM
No, I don't think you have done anything on Quora for $6$ days.
Upvotes, comments, and the like.
 
i rarely upvote and/or comment
i mostly just read
 
Oh....
I gather from the fact you follow Ernest W.Adams you're mostly liberal?
 
Isn't answering mathematics questions anywhere tiring?
 
i follow ernest w. adams?
i didn't know that
 
3:30 PM
@user21820 not at all
depending on the level of the audience, the same question can warrant a much shorter response on math.stackexchange than it would on quora
 
You have to be a lot more elaborate there...
 
Oh.
Not sure why you say "have to" though.
 
@S.C.B. ah, i see
i remember now
 
So, are you liberal?
 
i don't agree with most of what ernest w. adams writes, in fact, i don't think ernest w. adams has written a single answer that i can recommend or cite without reservation
 
3:32 PM
I can agree with you on that.
 
and that's why i follow him
 
He's too far gone to the left side (sounds like the dark side), but I think you can get what I mean.
 
i do
i don't think reading things that you agree with is a useful exercise, or a worthwhile use of your time
 
@wythagoras hello
 
Yep, I try to read arguements of both sides. I try to follow both
 
3:34 PM
Heh but it's useful to read things written by people you believe are reliable, right?
 
I am busy at the moment
 
Such as scientific articles.
 
@S.C.B. i am not sure who said this, but someone once made this remark: "the status quo is that liberals mostly read left leaning newspapers, and conservatives mostly read right leaning newspapers; but if you look at it logically, it should be the exact opposite"
 
lol.
 
"both of these groups should be looking for arguments against what they think, not for what they think"
 
3:35 PM
I try to read newspapers that are close to the center.
Is NYT or Reuters a reliable news source?
 
i don't think there's a single source i can cite without any reservation right now
 
@Starfall Yes to this. I do this most of the time.
But I still think there is much value in reading things from authors you generally agree with, as well.
 
@S.C.B. the best you can do is to read multiple sources, they all give you a part of the picture
 
What news sources do you think are more reliable by the way?
I'm curious because I'm not from the US.
So I can only look in from the outside so to speak.
 
Well, I personally found this article interesting, though I don't consider it accurate.
 
3:37 PM
@user21820 on any given issue, my trust in a specific institution is inversely proportional to my perception of how much incentive they would have to lie about a specific topic
with different topics, i trust different institutions
 
Ahh that's exactly what I keep telling people around me!
Like when it comes to health benefits of XXX...
 
i always keep in mind that they could be lying for reasons i am not aware of, though
so, obviously, i never trust any one source completely
 
Yea.
 
but some people draw the line from this to saying that "since they could all be lying, they are all equally valid sources"
 
Hahaha..
 
3:39 PM
Well, also many people are lazy...
 
that there's some notion of "equivalence" between some guy blogging on tumblr and a respectable media institution such as the wall street journal, say
and the wall street journal has published many articles which are completely inaccurate
i think they do this with malicious intent, even
but there's no "equivalence" here
 
They do it to further their own interests.
News sources are glorified ads.
They just want more views.
 
@S.C.B. yeah, and furthering their own interests sometimes involves trying to ruin another person's life and career
which would qualify as malicious intent
yeah
especially now, in the trump era, the public has been consistently losing faith in the mass media
this is reflected in the readership statistics of these newspapers as well
they have been declining for the last decade or so
and they are at an all-time low now
 
Lol...
Everything recently seems to lead back to Trump.
 
Particularly, I am appalled at the sometimes extreme hatred toward countries like China and Russia.
@user21820 Trump certainly has
Been good for CNN.
Good for the NYT too.
The people who benefited most from the 2016 US Presidential Election
Are those from news companies.
Or, people from SNS.
 
3:44 PM
Hmm that's true I guess.
 
Hopefully, it will all blow over.
My country is facing a Watergate level scandal
at the moment.
I'm not American.
A milion people are taking to the streets,
And honestly said, it was the news companies that got the most out of it.
Or the candle shops.
(We had a candle sigil)
 
Oh.
 
@Starfall Unless I'm mistaken, the situation over in Turkey doesn't seem to good either..
There's still a lot on the news about that attempted coup.
 
@S.C.B. well, the attempted coup has little to do with why the situation is not good
 
Well, I don't know.
I honestly just read the headlines.
 
3:49 PM
turkey is in bad shape economically right now, and there's still a climate of uncertainty before the referendum on the recent constitutional changes
the USD/TRY ratio has been declining recently, which is a good sign
the attempted coup is only related to the (still ongoing) purge
it is being conducted with extremely sloppy standards, and as broadly as possible; but hopefully the people who have been rather absurdly accused for no reason will be exonerated once the trials begin
turkey doesn't have the luxury of purging its judiciary without a care in the world right now, they need all the judges and prosecutors they can find
@S.C.B. i don't see how the election was good for CNN
if anything, it was very bad for CNN, and it continues to be very bad for CNN
 
They got a ton of views.
 
yes
 
CNN's stock rose as well during this election, though it was admittedly minimal.
 
being publicly called "fake news" by the president of the united states is not a good sign
 
Trump's accusation had little impact on how much money they made.
 
3:54 PM
yes
but you're thinking short term
it had little impact now
 
Well, is there any news source he called a "reliable news source"?
 
CNN, like any other media outlet in the world, is declining in its viewership
yep
breitbart and infowars
 
Wow.
 
trump's accusations are general accusations against the mass media, they are not specifically directed at CNN
 
But I don't consider the reason the CNN has been declining a result of Trump.
I think it's just a general trend.
 
3:55 PM
yes, it is
 
Everything goes up and declines.
 
@S.C.B. the causal arrow here goes in the opposite direction
 
Yes.
 
 
2 hours later…
5:39 PM
:-|
27
A: Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?

Simply Beautiful ArtNotice that $$\left.\int_1^xt^ndt=\frac{t^{n+1}}{n+1}\right|_1^x=\frac{x^{n+1}-1}{n+1}$$ but at $n=-1$, we get division by $0$, and clearly this is bad. However, following this line of logic, we can take the limit as $n\to-1$ to get $$\int_1^x\frac1tdt\stackrel?=\lim_{n\to-1}\frac{x^{n+1}-1}{...

Why so many upvotes though?
 
idk
ok seriously somebody stop flagging
 
More flags; might be time to take out the trash.
 
@SimplyBeautifulArt beacuse latex looks cool?
 
Y,all flage handlers, you neglected to delete some pretty offensive comments.
 
5:41 PM
no, we decided not to
 
@Mithrandir oh lookit i already took out some trash
 
@Riker lol, we're mathematicians, so it's normal to us
 
@amWhy because the guy who posted them understands now probably
 
next trash-removal is an orbital strike
so let's move on :P
 
@SimplyBeautifulArt hnq isn't tho
the people who see it on the main page of hot network questions aren't
and latex looks fancy to them so "ooooooooh upvotes"
 
5:42 PM
Lol
But why is my answer hot now?
It's many days old
 
no clue
 
:-/
So what subjects do you guys do?
 
@SimplyBeautifulArt working on precalc right now actually
for school
 
@Mithrandir whoa whoa whoa, you sure you didn't remove anything important?
@Riker ah cool. Good luck
 
5:49 PM
thanks!
 
Please, there's other ways of referring to users other than as "guy/s"
 
@SimplyBeautifulArt all from the political debate.
 
@amWhy my bad!
Ok thanks @Mithrandir
 
@amWhy to be grammatically correct "he/guy" is the pronoun for unknown genders
"they" is technically bad grammar for a single person
 
You can always use Zie.
 
5:53 PM
lol
 
I hate the "they" thing too, but "he" is no longer considered generic. Anyway, I'm out of here.
 
@SimplyBeautifulArt how about you?
 
Lol, cool
 
@amWhy see ya!
 
@amWhy bye!
 
5:54 PM
Grow up, Riker!
 
?
wot I do
 
@Riker I'm in history. I like to study math. You know, things
 
ah, cool
 
*eyebrow* Nothing wrong with 14 year olds.
:P
(I'm 14.)
 
mith likes eyebrows
*eyebrow*
 
5:55 PM
I'm 17
 
ah nice
 
If you wish, I don't mind teaching you calculus btw
 
sure! let me finish this worksheet first tho :P
 
Lol
@Riker what time is it?
 
I'm in CA, USA
it's 10 am
 
5:58 PM
Ok
 
o_O It's 8pm here.
 
So, I think I missed @Riker's comment. I think she's a bit naive, but she's okay, too.
 
o_O
what
 
You're a great gal, @Riker, no offense intended.
 
6:01 PM
whatever, I'm outta here
 
@SimplyBeautifulArt :-P
 
@amWhy so how was your day?
 
@SimplyBeautifulArt Well, I'm still in the middle of it, so I won't know for another six ours or so. So far so good!
 
XD ok
Mines gonna suck. I have homework to do once I get home
 
6:06 PM
Got it... I read your comment to quickly!
 
Mhm
Get to work out some passwords while I'm at it
 
I somehow "saw" "to do" as "due"
 
Because I'm stupid and use long random passwords
@amWhy same either way lol
 
6:43 PM
are "political debates" against stackexchange chat rules?
 
7:03 PM
It's the condemnation of a world religion, in its entirey, and evangelizing its evilness (recruiting extremists to believe your extremism, through offensive language and fake news, and cannot be justified as political, that violates site/chat rules.
 
@amWhy so, condemning a world religion is against chat rules?
is there some place where these rules are written?
i want to check for myself if "condemning a world religion in its entirety" is in there
 
If you do it on a math chatroom, yes. Peruse SE sites that may support your hate. Oops, there aren't any. Ask meta SE. Don't try to hijack a MSE chat.
I need to leave now....
 
@amWhy "hate"
@amWhy that's funny, because i don't think i saw you ever talk about math in this chatroom
i suppose you should be banned also
 
7:26 PM
@Starfall When they start raising flags and getting heated/offending people, then yes.
 
@Starfall read please:
351
Q: If you're gonna talk Politics, you must respect those who disagree

Shog9This is sort of a follow-up to two past discussions: Toward a philosophy of Chat Does the Be Nice policy require SE users to "be nice" to people who are not SE users (e.g. public figures)? Over the past year, there's been an uptick in discussions of politics in chat. JUST LOOK AT THIS CHART! ...

Someone tells you a topic - or the way you're discussing it - is being bothersome, that's a good time to either drop it or take it into a different room.
 
@Shog9 nobody told me that
 
You learn something every day :)
 
in fact, when you came in here and deleted the entire conversation, the conversation was already over
 
Yes, but it had started raising flags.
 
7:29 PM
@Mithrandir ...and nobody said anything about how the subject was inappropriate - whoever was flagging those messages could surely simply say "i think this subject is inappropriate, could you take this discussion somewhere else?"
@Shog9 i am going to go ahead and say that i did not show any sort of disrespect towards anyone who disagreed with me in that discussion
@Mithrandir also, are you saying that offending people is against the rules?
 
@Starfall yes.
 
okay, so if i find something offensive, can i have it deleted from the chatroom, and get the account of whoever said it suspended?
 
Technically, yes...
A good idea would be to stick with messages that you are sure that nobody would be offended while reading.
 
great, i find what you just said offensive
can you please suspend your own account?
 
see, this is why folks don't speak up and flag instead - they don't want a tedious argument.
7 mins ago, by Shog9
Someone tells you a topic - or the way you're discussing it - is being bothersome, that's a good time to either drop it or take it into a different room.
That's just good manners.
 
7:36 PM
O.O
Uh...
@Shog9 well, will he be able to be back?
 
@SimplyBeautifulArt he is now.
It was only for 1 minute.
 
@Shog9 again, nobody told me that, and i would like it if you stopped pretending that i was told this in advance
 
@Starfall I didn't. I gave you the information you needed, and left.
You keep pinging me instead of reading it.
 
7:40 PM
Starfall: Nobody's holding it against you, but now you're informed, and can avoid more drama :)
 
@Mithrandir i have no intentions of avoiding drama
and the more you keep kicking me, the more you are lending validity to my position
@SimplyBeautifulArt you should also join in this drama
you don't find this kind of drama every day
 
@Starfall You run the risk of fiercer and fiercer suspensions then when pepole start flagging content.
That's what Shog wants to avoid.
same with everyone else
 
@ThomasWard i don't particularly mind if i am suspended or not, i am trying to get you to understand that the way you deal with these "infractions" is fundamentally flawed
that was the whole point of my "suspend your own account" message, but it appears that this point was not delivered very well
 
@Starfall Then take up the handling of chat policies on Meta.SE. Until you hear otherwise, lay off the drama.
 
@ThomasWard you are the people who decide if something should be deleted or not
if i am not going to discuss this with you, who on earth am i supposed to discuss it with?
tell me, and i will go there
 
7:53 PM
the SE team, via meta.se? Oh wait, Shog is an employee of StackExchange and said "Knock it off".
There is no higher authority than SE employees.
 
yeah, as long as you acknowledge that this is an argument from authority, i have no problems
 
We're trying to avoid offending people here, and trying to keep the place friendly for everyone. If you're insulting my religion, I don't feel comfortable - same with political discussions.
 
Or insulting anyone for any reason.
It violates the "Be Nice" rules. Which we enforce. We being all moderators.
You've been told to knock it off with the drama. By many people with the capacity and requirement to enforce "be nice". You violate that rule at your own risk. (So, knock it off, and don't keep going with drama)
4
 
So basically, please keep the conversation civil and pleasant for everyone.
 
@Mithrandir you have successfully coerced me into not even being able to say what i think about this policy, because you are implying that if i do, i will be banned; so criticizing site policy in this chat is not allowed either, it seems
fair enough
 
8:06 PM
@Starfall The Be Nice policy is non-negotiable, yes. It's a fundamental Stack policy.
@Starfall Also, why would you argue against a policy that aims to make the experience pleasant for everyone?
 
@Mithrandir because it's not possible for you to make the experience pleasant for everyone, you're making it extremely unpleasant for me right now; and this will be so for anyone who wants to speak his mind about a controversial issue in one of these chatrooms
 
351
Q: If you're gonna talk Politics, you must respect those who disagree

Shog9This is sort of a follow-up to two past discussions: Toward a philosophy of Chat Does the Be Nice policy require SE users to "be nice" to people who are not SE users (e.g. public figures)? Over the past year, there's been an uptick in discussions of politics in chat. JUST LOOK AT THIS CHART! ...

 
i do respect those who disagree
 
Yes. But when the discussion starts raising flags, you should think about what you've said.
 
yes, i said something controversial that some people could find offensive, that's not the same thing as not respecting someone who disagrees with me
 
8:10 PM
Please avoid saying things that can offend other people.
5
That's what I'm trying to say.
 
@Mithrandir yes, so this is not about respect at all, it's about not hurting other people's feelings
 
Which is a part of respect.
 
it is not
it's the exact opposite of respect to not tell someone what you think because you think their feelings can't handle it
if you're honest about your site policy and stop dressing this up as "respect", i will be glad to abide by it in the future
 
Okay. The site policy is to not offend anyone and keep the experience positive for everyone. Controversial topics can offend people very quickly.
2
 
great, thank you for the information
also, who keeps starring @Mithrandir's posts? i am curious
 
 
1 hour later…
9:28 PM
@SimplyBeautifulArt Maybe you should read posts more carefully before replying with "lmao" and such, lest such replies are taken as support for offensive comments in "your" realm. From now on I'll take your "lmao" or "lol" or :D etc, in response to comments left here, as a stamp of approval and/or agreement from you wrt others' comments. If you simply don't want to acknowledge offensive comments, then ignore them, just don't use lol as a method of avoiding them.
 
 
1 hour later…
10:57 PM
@ArtOfCode Oh, hello and welcome to my realm!
 
11:39 PM
$$\huge\color{#ff77dd}\heartsuit$$
 
@Deedlit @Wojowu @user21820 We have a new submission!
 
i know its smaller than all their submissions, but i still wanted to submit it
 
@chronolegends I can't actually judge, since everyone is making such large numbers
@chronolegends You never know :D
 
I checked c: so i know its the smallest one lol
 
11:50 PM
lol
 
its roughly 2^^^^^^^9 < X < 2^^^^^^^^9
 
Ah... ok
You know, if you figured out how to produce a(^b)c, you can make much bigger numbers
 
i'm working on something bigger (169 chars left :D) but i thought you might appreciate an entry that wasnt mind boggingly huge lol
 
11:58 PM
Think you next number is going to compare size-ably?
 
it might
Thanks for accepting my submission, i g2g :) cya!
 

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