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• CommentAuthorAnixx
• CommentTimeMar 5th 2012

1.

Well, it's not spam in the sense of unsolicited email. It is, however, written with blatant disregard for both the explicit and unwritten rules of how the site works. You can't just write down a bunch of unmotivated formulas, not explaining where they came from and ask whether they are in the literature or not; do you even know if they are true? It's unclear from what you've written. If you want a good answer, you have to put real work into explaining what you want to know and what context that fits into. There's no reason you can't ask questions about whether a particular identity is known or not, but you should do it one (or maybe one class) at a time, and there should be sentences in the question.

• CommentAuthorAnixx
• CommentTimeMar 5th 2012

Of course I am sure they are true/
2.

Well, you should say that explicitly in your post, as well as why (have you written proofs? Are they easy? Hard?). That's just an example of important context you've left out.

• CommentAuthorAnixx
• CommentTimeMar 5th 2012 edited

It seems that this post http://meta.mathoverflow.net/discussion/1319/lots-of-spam-today/ has contributed to the closing this question. Before it my question was not downvoted despite over 150 views. And Andy Putman still did not explain his point of view other than "the system is overflowed with semi-spam questions" and putting my question as an example of semi-spam.
• CommentAuthorMariano
• CommentTimeMar 5th 2012

Isn't Ben's explanation above satisfying? Odds are Andy's would differer little from it.

3.
I don't see why this question is inappropriate. I don't see why we have to see his proofs - even just seeing if the statements are new is interesting. I think it is reasonable to see if anyone on the site knows any of the formulas listed, or has a good idea about where to find out. I think it is only because of prior history that Anixx is getting this question closed, which I don't think is really fair. Does it fit the the FAQ?

It is focused: He wants to know whether these specific formulas are new
It has a definite answer: Either they are or they are not
It is research level: I don't think many undergraduates would think about such things, and it is relevant to Anixx's research to know if these are new or not.
It benefits from being looked at by a wide audience: MO is great for pooling a large number of experts who might know the answer.
4.
it seems the major objection is that Anixx hasn't included "enough sentences". I feel that I understand the question completely without further explanation.
5.

Steven, Ben hasn't asked for proofs. It appears to me he's just asking for context, and I think that's pretty reasonable. Putting in a word or two explaining what a formula means, so that it's intelligible to a typical mathematician would be a good thing.

My impression is we generally expect people to write-up their question rather than asking people to read an entire paper before a post makes sense.

6.
Your post was a list of ten formulas without context or explanation. Moreover, to understand the notation in them you had to go and read a paper. Given that you have been posting here for a while and are thus presumably familiar with the community norms, you had to know that this was (to quote Ben) "written with blatant disregard for both the explicit and unwritten rules of how the site works". Can you think of any other question of this form which was well-received by the community?
• CommentAuthorAnixx
• CommentTimeMar 5th 2012 edited

What notation should I explain? It's conventional and where it is not, there are words describing the meaning. Well possibly if you do not understand this, you are far from this field and you have little to contribute to the answer so let the others to do so.

What is even more striking is that you explained the question as a part of the "spam overflow" so to persuade other people to take action against it rather than just voting for yourself.

I even doubt whether the "spam wave" was real or just invented to advertise attention to this question.
• CommentAuthorWill Jagy
• CommentTimeMar 5th 2012 edited

For what it may be worth, I thought the spam wave referred to the recent Ph.D. from Morocco, who has some serious anger issues. That is, of course, assuming that the MO presence is the same person whose name and picture (and, initially, a website with his professional info) appear. If not, that would be one ugly deed, stealing someone's identity (as far as MO is concerned, anyway) and posting items guaranteed to piss off the users. The only similar example I know is on Facebook, a grown man, visiting his mother, typed some (very mildly) unflattering stuff about his sister on his mother's Facebook account. It took the mother a day to put up a correction. I do not believe she understood how awful the situation appeared to those outside her house.
7.
It seems clear that Anixx is not capable of understanding the standards you are holding him/her to. I don't know why, but it doesn't seem like a deliberate choice: There is every indication that Anixx simply does not understand what you want him/her to do to get these questions and answers up to standards. Does this mean we should prohibit Anixx from using the site? I for one would be glad to put up with it to keep him/her around.

I think a big part of the problem is that we all develop a "crank alert system". John Baez even assembled a list of criteria to detect a crackpot. Usually these heuristics work pretty well, and if you see a question posted in a certain style, you close it - hoping to deter the crank from coming back and bothering you. This case is very different. It turns out that, even though your warning bells are going off, the actual question is substantive. The user asking the question has a unique set of skills and abilities (Anixx seems to be really good at working with "complicated formulae", and generating novel results). Browsing through Anixx's user page, I see a lot of interesting stuff. Sure, I would like to have more knowledge about where these formulae come from, but they seem legit. I think we need to mentally add an exception for Anixx to our "crank alert systems", because he is not really a crank.
8.

Steven, we've had many very long discussion threads with Anixx on this forum before. It's not clear to me if you're familiar with them but here are a few. A google search will provide you with more:

http://meta.mathoverflow.net/discussion/756/tetration/

I suspect Anixx is a little stubborn, knows and understands the concerns people are raising, but simply refuses to address the general standards people want to see on MO.

I think you're correct in that Anixx is not a crank -- I believe there are several MO users that know him personally. I do not. I think the forum is tolerant of many eccentricities among posters but my general impression is people want to hold the line on the posting of giant formulas with little context. I generally agree with this seeming consensus.

• CommentAuthorDL
• CommentTimeMar 5th 2012

I essentially agree with Steven Gubkin here; hence my (attempt at a conciliatory) comment on the post in question. I personally don't think that MO should be used as a replacement for a literature search. On the other hand, with a few extra sentences this question would have been no worse than many that no one votes to close.

@Anixx: That said, it couldn't hurt to put in a few minutes and try to make your questions more pleasant/easier to read. I think that MO users in general are much less inclined to close a question they understand than one they don't.
9.
Will Jagy is correct that the main thing I was referring to was the burst of bizarre posts (now mostly deleted) by a "recent PhD from Morocco" (and I agree that given the possibility of identity theft we should not post his name here).

I should add that my take on this is very similar to Ryan's. I don't think that Anixx is a crank, just someone who is stubborn. But I think it is important to uphold certain minimum standards for questions. Given its completely generic title (How much these results are new?) and complete lack of written context, I cannot imagine that any relevant experts would even be able to find this question.
10.
Andy, if the title bothers you, you can always edit it to something more likely to show up in an ezpert search.
11.
@Gerry : The title was just a tiny part of what was wrong with the question, and really I could not see a way of saving it. Fixing the title seemed kind of pointless. There's a reason that it got 5 downvotes (none of which, by the way, was mine).
12.

@Anixx

I did not vote on the question, but although I think there are several (yes, several) perhaps interesting questions in there, they are not presented in an appealing manner.

The notation $\Pi_x$ and $\Sigma_x$ is not explained. You clearly cannot be taking the summation over all $\mathbb{R}$. Thus $x$ is presumably an integer, and possibly a non-negative or positive integer. Also the summation range may vary between equations.

$\psi^{(n)}(x)$ is not explained, though if it is a standard function, it might be helpful to say what it is.

If these equations are the result of your work, Anixx, please say so, and perhaps provide some information on how you found these. I would be happy to see (focussed) questions about this topic if these issues were addressed. Note that splitting each equation into a single question with little motivation might not go down well.

EDIT: Perhaps linking to a reference/definition of your discrete (multiplicative) integrals would help. I'm not interested enough to search it out myself, but if you provided a link, I might follow it.

• CommentAuthorAnixx
• CommentTimeMar 6th 2012

@Andy Putman, so even if you did not vote on the question, you specially put an attention at necessity to close it as an example of "spam wave". I am in no way associated with your Morocco PhD, but you put the question as if it was in some way associated and asking people to help with handling the spam overflow.
• CommentAuthorAnixx
• CommentTimeMar 6th 2012

> The notation $\Pi_x$ and $\Sigma_x$ is not explained.

You are wrong, it is clearly said it is antidifference in the text of the question. How can I explain it better? It is the standard notation for antidifference, used by say Mathematica and Wikipedia.

> $\psi^{(n)}(x)$ is not explained, though if it is a standard function, it might be helpful to say what it is.

You are wrong, in the text it is said it is polygamma. Can you read?
13.
Anixx, "Can you read?" is entirely uncalled for. If it were up to me, you'd be suspended on the spot for that.
• CommentAuthorgata
• CommentTimeMar 6th 2012 edited

Anixx, it would probably have helped if the question had started as follows:

The antidifference operator (also known as indefinite sum as analogy with indefinite integral) is the inverse of the difference operator delta(x)=f(x+1)-f(x), analogously to the antiderivative being inverse of the derivative. See for example previous question on tan x http://mathoverflow.net/questions/41011/what-is-the-indefinite-sum-of-tanx/42903

http://en.wikipedia.org/wiki/Indefinite_sum

Multiplicative integration uses Riemann products instead of Riemann sums, see for example the question: http://mathoverflow.net/questions/32954/multiplicative-integral-of-gammax/42611

The discrete analogue of this would be quotient and antiquotient operators, the antiquotient being called the "indefinite product" by software such as Maple and Mathematica just as they also use "indefinte sum" for antidifference.

http://en.wikipedia.org/wiki/Indefinite_product

In what follows, the terms "discrete integral" and "discrete multiplicative integral" will be used for "antidifferece/indefinite sum", and "antiquotient/indefinite product" respectively.

Then you can say you've found some formulae.

However if you did this then some people would say "too long didn't read" so it's a case of "Damned if you do, damned if you don't!"

The multiplicative integral of gamma x isn't new in the sense that you yourself wrote that formula back in 2010 in the question:
http://mathoverflow.net/questions/32954/multiplicative-integral-of-gammax/42611

Your formulas for the "discrete multiplicative integral" a.k.a. antiquotient, antiratio or indefinite product, are, I would guess, new in not being published before, since it is such a niche topic, although see the xkcd forum topic: Calculus of finite ratios? http://forums.xkcd.com/viewtopic.php?f=17&t=25365

For your fomulas for antidifferences, I would contact by email the authors of recent papers or books on the topic of "indefinite summation" and ask their opinion if you don't get answers here.

"Finite ratio" is better term than "finite quotient" since "finite quotient" tends to be used by mathematicians in the abstract setting of quotient of some space by another.

And remember that the human race are a bunch of idiots and always will be, so there's no point getting angry if you are misunderstood. Nobody wants to jump through hoops - no matter how large they are or how low to the ground - just say "Taking psi(x)= balanced ..."
14.

I have to agree with some people above that calling it "spam" is a bit extreme... while agreeing that the question could stand improvement.

Suppose MathOverflow had been around about 100 years ago and Ramanujan posted a bunch of his formulas, asking if they were already known. Would his question have been closed as 'spam'? (Of course, something like that did happen -- his stuff wound up in some trash bins before Hardy and Littlewood entered the story.)

• CommentAuthorAnixx
• CommentTimeMar 6th 2012 edited

@gata If I was posting in a forum of scoolchildren I would explain any sign and function of course as you suggest. But this is a forum of experienced mathematicians, and I expect them to understand something not less than an undergraduate. I was surprised that many people asked what is polygamma function in one of my previous answers. This is normal that some people do not understand: I for example do not understand many questions and answers in MO, but I do not demand all them to close because of that. If you do not understand something you are likely have nothing to contribute to the topic, so just pass along.
• CommentAuthorgata
• CommentTimeMar 6th 2012 edited

Although you might expect a reasonable number of people to be familiar with the calculus of finite differences and the term "antidifference", I doubt many would have known the term "discrete multiplicative integral" - except of course in today's world Google is only a click away and a simple Google search does bring up the relevant Wikipedia page as the very first result: http://en.wikipedia.org/wiki/Indefinite_product

Still, the point is "discrete multiplicative integral" is not standard terminology, the software packages call it "indefinite product". (although even that is problematic without definition, for example "indefinite sum" has caused confusion on MO before due to having more than one meaning.)

In any case, on MO, as elsewhere, it would be good practice to at least link to definitions like so:

<a href="http://en.wikipedia.org/wiki/Indefinite_sum">Discrete integrals (antidifferences)</a>

<a href="http://en.wikipedia.org/wiki/Indefinite_product">Discrete multiplicative integrals (antiratios)</a>
• CommentAuthorMO Scribe
• CommentTimeMar 6th 2012

To answer the original question, all the formulas are trivial, uninteresting, and essentially formal consequences of the definitions of the functions involved. To ask if they are "new" somehow misses the point - they can all be derived easily if one wants to --- the *hardest* part is actually knowing the *definition* of the polygamma function for negative arguments. One might as well ask whether the formula
1298312938 * 208371825 = 270531836312171850 is new or not (probably it is new, certainly it is not interesting).
15.
Todd, perhaps I could refer you to Bob Dylan's 115th Dream, http://www.bobdylan.com/songs/bob-dylans-115th-dream;

I said, “You know they refused Jesus, too”/He said, “You’re not Him...."

Also perhaps relevant is this quote from Carl Sagan, seen at http://en.wikiquote.org/wiki/Carl_Sagan:

The fact that some geniuses were laughed at does not imply that all who are laughed at are geniuses. They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown.
• CommentAuthorMariano
• CommentTimeMar 6th 2012

They laughed at Fulton?

16.

Gerry, it looks like you misunderstood my point. It seems that the main objections to the question were based on its form, not its content. Right? And that form (of listing formulas without explanation) bears some comparison to the form adopted by Ramanujan, even if there is no comparison in terms of sheer brilliance in content.

As I said, I thought the presentation could be improved (and arguably this could be said of Ramanujan too). But I don't think that "spam" is quite fair. I think I agree with what Steven Gubkin has said.

• CommentAuthorMariano
• CommentTimeMar 6th 2012

Did Ramanujan write in that style when communicating with others?

I would have thought that the famous diaries, with its lists of extraordinary formulas, were not intended to be read by anyone but him...

17.
Mariano, Ramanujan's original letter to Hardy is probably available somewhere. Two pages are reproduced on page 150 of Kanigel's biography of Ramanujan. Page 1 is largely expository. On the other hand, page 9 goes, "Theorems on Continued Fractions. A few examples are..." and the rest of the page is filled with formulas. I think all the notation in the formulas would have been familiar to the mathematicians of the day.
18.

Google books gives me the first 4 pages of Ramanujan's letter. Even if later pages are merely filled with formulas, there is a decent amount of text to start with. But Todd has a point. The exposition could be improved (and it would have been better to improve it based on comments before all this escalated) but on the face of it there is a question there. Making the title relevant would have attracted the attention of experts quicker. And now we have an answer to the actual question.

But I bow out of this conversation, I have said my piece, and add my voice to gata's first post.

19.

@MO Scribe: before concluding the formulas are new, one should consult a large number of papers that can be found in MathSciNet ... for example, likely titles:
Sofo, Anthony, Sums in terms of polygamma functions. Bull. Math. Anal. Appl. 2 (2010), no. 3, 40–52.
Boros, George; Espinosa, Olivier; Moll, Victor H. On some families of integrals solvable in terms of polygamma and negapolygamma functions. Integral Transforms Spec. Funct. 14 (2003), no. 3, 187–203.
Nishimoto, Katsuyuki; Tu, Shih Tong Fractional calculus of psi functions (generalized polygamma functions). J. Fract. Calc. 5 (1994), 27–34.

• CommentAuthorgata
• CommentTimeMar 7th 2012

Just some notes:

Search terms: "indefinite summation" OR "symbolic summation"

Papers:
* Symbolic Integration And Summation Using Homotopy Methods, Bernard Deconinck And Michael Nivala

* Groebner bases, symbolic summation and symbolic integration, F Chyzak

* Symbolic Summation in Difference Fields, Carsten Schneider
20.