Talk:List of formulae involving π

message: I have created the article. Regarding the name: Wiktionary says "formulae in scientific use, formulas in informal use." - but if anyone objects (or to any other aspect of the name), we can move. In any case, we can place here all the forumlae that are interesting, but not important enough to be included in Pi. I've placed a few formulae for starters. Of course, comments and expansions are welcome. -- Meni Rosenfeld (talk) 09:24, 7 April 2006 (UTC)
thread_title: Article created

message: Apart from the burning question whether it should be "formulas", "formulae", or "formulæ", involving "Pi" or "π", isn't the notion of "involving" somewhat broad? What about sin n π = 0 and arctan 1 = π/4? Does that belong here or not?
:Yes, I also think that the title of the page is too broad and the word 'involving' should be removed from the title to be replaced by some more appropriate word. Deepak.sachan 22:44, 8 April 2006 (UTC)
replies: text: I'm open to suggestions. -- Meni Rosenfeld (talk) 06:10, 9 April 2006 (UTC)

text: I guess every formula involving pi can be be used to define it, with sufficient conditions. For example, for sin π = 0 you can define: π is the smallest positive number such that sin x = 0. So I don't know how much can be worked out from such a criterion. The criterion should probably be how interesting and elegant the formula is, while trying to avoid too many formulae around the same theme. So it's okay to write π/4 = arctan 1 and give a series expansion, but we wouldn't write it as the arctan of every possible number. Although we probably would include several efficient Machin-like formulae. -- Meni Rosenfeld (talk) 17:35, 8 April 2006 (UTC)
thread_title: Article name

message: Is the new formula by Fredrik really notable? It is basically just a discretization of \int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}. -- Meni Rosenfeld (talk) 12:55, 4 May 2006 (UTC)
replies: text: It's not mine; it's the Borweins'. Regardless of whether it is trivial (I think not), the fact that such approximations can be constructed at all is certainly noteworthy. Fredrik Johansson 13:57, 4 May 2006 (UTC)

text: That's a bit like omitting 355/133 because it's just a truncated continued fraction, or for that matter, log(6403203+744)/1631/2 because it's easily extracted from the series expansion of the j-function. It may be obvious to you, but that's because you already know the math behind it. Most readers won't. It'd be more helpful to amend the section with an explanation. Fredrik Johansson 14:39, 4 May 2006 (UTC)
thread_title: New approximation

message: Would the page titles Formulae involving π or Formulae using π be more appropriate for this article? Deathbob 07:28, 15 January 2007 (UTC)
replies: text: I think not. The prefix "list of..." is common for pages which are, in fact, lists. -- Meni Rosenfeld (talk) 17:54, 15 January 2007 (UTC)
thread_title: Name

message: after reading the AFD discussion (Wikipedia:Articles_for_deletion/List_of_formulae_involving_π), i was thinking it'd be good to have a prose description at the top of the article of what types of formulas are in the article. that is, explain that only certain formulas of historical significance or intellectual significance appear here. (or whatever criteria editors want to set.)
links to related articles are nice, too, and many of the formulas already have them. on a quick glance, i noticed the borwein formula for hexadecimal digits of pi doesn't have a link. hasn't some mad pi fanatic already created a wiki article on that? ;)
cheers,
Lunch 17:45, 25 January 2007 (UTC)
replies: text: It probably should have been deleted. There's still nothing important here. (But don't waste time discussing it.) -A876 (talk) 22:05, 14 May 2014 (UTC)
thread_title: a suggestion

message: It is unconventional to use a math symbol in a title even when that symbol is universally understood. It's Three Blind Mice, not "3 Blind Mice", a Dirac delta function, not a δ function, and so forth. In this case, "pi" is a far more common usage than "". On Google books, the formula pi -wikipedia gets vastly more hits than formula π -wikipedia. CNN uses "pi", the BBC uses "pi", and the New York Times uses "pi". The entry in Britannica is entitled "pi," as is the entry in Merriam-Webster. Math journals can go either way. Check here and here for journal articles with "pi" in their titles. Kauffner (talk) 04:10, 19 April 2011 (UTC)
replies: text: It was NOT moved (apparently not officially proposed). It remains at "List of formulae involving π". -A876 (talk) 22:05, 14 May 2014 (UTC)
thread_title: Explanation of move from "{{pi}}" to "pi"

message: There is a move discussion in progress on Talk:Liu Hui's pi algorithm which affects this page. Please participate on that page and not in this talk page section. Thank you.  —RM bot 07:16, 27 April 2011 (UTC)
replies: text: It was moved to "Liu Hui's π algorithm". It remains there. -A876 (talk) 22:05, 14 May 2014 (UTC)
thread_title: Move discussion in progress

message: There is a move discussion in progress on Talk:Pi which affects this page. Please participate on that page and not in this talk page section. Thank you.  —RM bot 13:15, 2 June 2011 (UTC)
replies: text: It was NOT moved. It remains at "Pi". -A876 (talk) 22:05, 14 May 2014 (UTC)
thread_title: Move discussion in progress

message: Under Other infinite series and with \zeta(2n), is there a source for this equation? What does the B_{2n} mean? John W. Nicholson (talk) 02:29, 22 September 2013 (UTC)
thread_title: Is there a source for this?

message: The second formula (wrongly written) and the last one of the table of the section "Infinite Series" are the same formula. The formulas in the table are the 17 series given by Ramanujan, however one is lacking: the one with 1103 (which is in the Section "Efficient Infinite Series"). All the formulas in the table should be written in the same way: using the rising factorial. A better title for the section "Infinite Series" is "Ramanujan Series". The first one and the last one of the formulas in "Efficient Infinite Series" are not very efficient because there exist formulas much more efficient than those.
J314G (talk) 09:48, 14 July 2017 (UTC)
replies: text: If you notice any errors, you can always just go ahead and fix them.  As far as "efficient" goes, yes, it's probably a bit vague anyway.  Normal factorials should be used in place of rising factorials if appropriate (I'm assuming you mean writing (1)_n in place of n!).  This is how they're given in the source anyway.  And yes, the section titling and organization here is definitely kind of wonky.  --Deacon Vorbis (talk) 14:09, 14 July 2017 (UTC)
replies: text: I mean that inside the table the formulas are written sometimes with factorials and other times with rising factorials. There is an equivalence, for example (4n)!/(n!)^4 is the same than (1/2)_n(1/4)_n(3/4)_n / (n!)^3 * 256^n. I think that all the formulas in the table should be written with the same symbols, either all with ordinary factorial or either all with rising factorial which   the exceptional case of (1)_n which is more frequently written as n!. The writing with Pochhammer's symbols has some advantages, however ordinary factorial are wider known.   J314G (talk) 15:13, 14 July 2017 (UTC)
thread_title:  Some things that should be corrected 

message: Would it be possible to add a reference with a demonstration for the nice alternating sums of reciprocals of the odd numbers?
It would be nice to understand the deep meaning under the reported fact that
\sum \left(\frac{-1}{2k+1}\right)^k \propto \pi^k. Giacomo Lanza (talk) 21:06, 30 April 2021 (UTC)
replies: text: I've just added a reference. A1E6 (talk) 20:56, 9 October 2022 (UTC)
thread_title:  Demonstration required: Sums of powers of reciprocals 

message: When f(x) is a piecewise continuous function having zeros at x_1 < 0 and x_2 > 0, but f(0) ≠ 0,  
\int_{x_1}^{x_2}\frac{f-xf'}{x^2+f^2}\,dx = \pi
is the integral of  \frac{d}{dx}atan\left(\frac{f}{x}\right), and always yields \pi. The proof is obtained by confirming that the integrand is indeed the derivative pointed.
Hitsuji Santos(talk) 02:10, 7 September 2021 (UTC)
thread_title:  Integrals yielding π 

message: This form of the functional equation is quite tortuous (and maybe torturous) so that the two sides are equivalent exchanging s and 1-s. I would suggest the much simpler form at Riemann's functional equation in the article on the zeta function.
Natkuhn (talk) 22:29, 14 March 2023 (UTC)
thread_title:  functional equation of the Riemann zeta function (under Miscellaneous) 

message: Title, both are not equal to pi. The second one is close, but I don't know why the first one is there. If someone could prove me wrong, that would be great. 131.106.140.129 (talk) 05:44, 26 June 2023 (UTC)
thread_title:  Last two Jacobi function pi equivalencies are inaccurate