Mathematics

12:01 AM

@robjohn you can say so (in a way yes) .. but this time I have managed to get closed forms of $\sum\limits_{n=1}^{\infty} \frac{H_n^3}{n^3}, \sum\limits_{n=1}^{\infty} \frac{H_nH_n^{(3)}}{n^2}, \sum\limits_{n=1}^{\infty} \frac{H_nH_n^{(2)}}{n^3}, \sum\limits_{n=1}^{\infty} \frac{H_n^2H_n^{(2)}}{n^2}, \sum\limits_{n=1}^{\infty} \frac{H_n^4}{n^2}$ with series manipulation alone .. no integrals, no polylogarithms :-)

ah and $\sum\limits_{n=1}^{\infty} \frac{H_n^2}{n^4}$ and $\sum\limits_{n=1}^{\infty} \frac{H_n^{(2)}}{n^4}$ could be mentioned as well .. but I think I did them b4 ..

robjohn

@r9m the ones that I did were with only series manipulations.

r9m

@robjohn yes!! :D all my inspirations come from your answers here! That's one irrefutable truth!

robjohn

@r9m Cool! I am glad to have been of assistance.

r9m

@robjohn It's more like you are the wise Gandalf! I am a hobbit :P

@robjohn is there a mail address I can mail to you (for when I wish to share some stuff that I can't share here? :) .. )

Carry on Smiling

1:13 AM

Hello

Adeek

2:29 AM

@TedShifrin I finished your first semester course. It was a delight. I am really grateful you put it on youtube. I enjoyed it a lot and some of its beauty.

Boolean_functions

Anyone know of any online calculators that convert propositonal logic expressions to ones using only the NAND operator?

user227867

6:08 AM

@r9m He didn't give me his address before, so I would be jealous if he did give you.

Agawa001

6:20 AM

moment recorded: room without moderators

robjohn

7:27 AM

@Agawa001 Ha!

Agawa001

7:46 AM

@robjohn that was shortlived

Agawa001

8:03 AM

@DanielFischer i couldnt really get ur proof in my perception maybe you could detail it in mathematical terms/symbols

it is too literary

Tobias Kildetoft

Does anyone have experience with CrossRef and OrcID? It seems to keep updating the same piece of work on my profile without actually changing anything.

Agawa001

or maybe i should pay more attention to it

robjohn

@r9m: another simple sum :-)

Daniel Fischer

@Agawa001 Take a piece of paper, sketch (part of) a grid, with arrows showing the direction of the outer edges, and see what happens when you give the inner edges directions (respecting the "two in, two out" condition), trying to avoid a square with oriented boundary.

r9m

@robjohn (+1) Awesome!! :D

robjohn

8:14 AM

@r9m are you on Dropbox? That is how Chris's sis and I transfer things.

r9m

@robjohn oh! I don't have dropbox (actually don't know how to use it) .. I use google docs to share stuff ..

Agawa001

@DanielFischer so from a small grid, things can be extrapolated by induction

r9m

@DanielFischer I might plan on cloning your brain when the technology arrives that is =P .. It was a very simple but elegant proof. Thanks!

bbl .. classes ryt now

Agawa001

@r9m unfornunately for me i cant read proofs where numbers and symbols are barely present

user 1618033

9:31 AM

@r9m All these series I've finished a long time ago. And my initial intention was to keep my tool only for my book, but well, I had to change my mind a bit.

By series manipulations only.

Agawa001

@user1618033 i have done tools for auto-scripting and intelligent converters, i didnt share em eithet they took me much time

my coworker requested them for money, he couldnt even find em in internet

user 1618033

@Agawa001 I see.

@robjohn about r9m posts. All these will be elementarily done in my book.

@robjohn together with advanced forms never done before.

@r9m it's good to say your inspiration comes from robjohn answers but don't miss the fact that without me you probably never did any of the series of weight 6 you claimed above you did.

r9m

10:17 AM

@user1618033 Your solutions are inspiration too :) I never forget that .. but you never showed me your series manipulation solutions to these problems and I did the weight 6 ones without using any of the tools you showed me ..

user 1618033

I simply don't wanna sound as a bragging or anything like that, but the simple thing is that I'm the first that ever did all series elementarily using an incredibly powerful tool not known to the present date (according to my knowledge).

@r9m You used the disguised form of Au-Yeung ...(it's the same story)

r9m

@user1618033 and extended it further (which is no longer the same story .. I've only showed you a part of it .. there's more that is required to get the other weight 6 sums)

user 1618033

@r9m Yeah, but that is a critical point also for the extention.

@r9m Just wait a second ...

\begin{equation*}
\sum_{n=1}^{\infty} \left(\frac{H_n}{n}\right)^2 \left(1+\frac{1}{2^2}+\cdots+\frac{1}{n^2}\right)=\frac{41}{12}\zeta(6)+2\zeta^2(3),
\end{equation*}

@r9m ^^^ an example

Which needs an extention, indeed. To get my point well. ;)

Anyway, this discussion leads nowhere. I'm back to my work, and promise in the future to be thousands times more careful about sharing stuff.

BBL

r9m

@user1618033 in that spirit the whole of mathematical development should be duely credited to those who laid the founding stones. If you claim that such development 'might' not be possible without those foundations .. that is a valid claim .. but don't say it'd be impossible otherwise :P

Tobias Kildetoft

Is there really any way user 1618033 could be more careful about sharing stuff? I don't think he/she has so far shared any of these amazing tools.

r9m

10:25 AM

@user1618033 nah ,.. no extension for that one ;) .. but $\sum\limits_{n=1}^{\infty} \frac{H_n^4}{n^2}$? yes .. atleast I needed to tinker and upgrade it a bit ,, :) (when I say upgrade you'll probably know what I mean .. it's just a recursive application of the previous au-yeung lemma right? )

user 1618033

@r9m $$\sum_{n=1}^{\infty} \frac{H_n^4}{n^2}=\frac{979}{24}\zeta(6)+3 \zeta^2(3)$$

BBL

For the record

I finalized \begin{equation*} \sum_{n=1}^{\infty} \left(\frac{H_n}{n}\right)^2 \left(1+\frac{1}{2^2}+\cdots+\frac{1}{n^2}\right)=\frac{41}{12}\zeta(6)+2\zeta^2‌(3), \end{equation*} in 3 different ways!

BBL (I'm out to buy some food for my dogs)

user 1618033

10:50 AM

@r9m Back. That lemma is indeed very powerful.

user227867

@user1618033 You misspelled extension.

user 1618033

@TobiasKildetoft If I showed you anything about my tools do you think you would be capable of properly assessing anything?

Tobias Kildetoft

Probably not, no

user 1618033

@JasperLoy You're right. Thanks.

@JasperLoy How are you doing?

user227867

@user1618033 I am OK. I did not make any videos today. I want to write some blog posts soon on my blog. It is currently empty.

user 1618033

10:53 AM

@JasperLoy Sing some more.

user227867

@user1618033 Yes, I certainly will. Now 4 videos. I will go to at least 20, maybe 30 eventually. On my blog, I would like to do book recommendations on various topics, non-math and math.

user 1618033

@JasperLoy awesome. Hope you'll add my book there too. :-)

user227867

@user1618033 Nobody would read my blog, LOL.

user 1618033

@JasperLoy I would read it.

user227867

@user1618033 OK, we will see about it when your book comes out.

user 1618033

10:59 AM

@r9m sorry if I seemed a bit tough, but so many things happened, and I simply worked like hell for all I got. That's why I'm talking with so much affection .

Nobody gave me any bit of help in all I did (related to the stuff in the book).

user227867

@user1618033 I won't talk to or talk about the user I mentioned yesterday anymore, but it suffices to say that he/she is the most evil person I have met online, abusing me and this site's users in the past and in the present in various ways.

user 1618033

@JasperLoy Maybe he/she is in love with you?

user227867

@user1618033 That is not relevant at all. And whether someone is mentally ill or not is also irrelevant. Abuse is abuse. Of course, I considered carefully before using the word abuse.

user 1618033

@JasperLoy maybe @robjohn can help?

user227867

@user1618033 Nope, this matter has got nothing to do with the moderators of this site, so let's not bother them.

user 1618033

11:04 AM

@JasperLoy OK

user227867

@user1618033 Anyway, this will be the last time I talk about this person, so let's forget about him/her right now!

user 1618033

@JasperLoy As you wish then!

user227867