Talk:Borwein integral

When less than half becomes apparent

The fact that the lengthy denominator is not exactly twice the numerator is obvious from the last four digits. If you look at the first digits, you need to get all the way to the 12th one to establish the fact. Should the article mention this somehow? Michael Hardy (talk) 18:39, 11 August 2010 (UTC)

I don't see anything especially significant about that, unless there is some subtlety I overlooked. No such significance is identified by the article or references either. So, nah, I don't think it bears mentioning.--FeralOink (talk) 09:01, 9 September 2018 (UTC)

Approximately versus equal to?

Can't we fix this article and use $\approx$ instead of $=$. That way all the integrals (even the limit) are $\approx {\frac {\pi }{2}}$, so that the symmetry of the equations is preserved? -- A concerned Mathematician.

As I understand it, the article is correctly using $=$ when it means $=$ and $\approx$ when it means $\approx$. The fact that some are exactly equal and then others are not quite is exactly what makes these interesting mathematically. --Qetuth (talk) 12:43, 24 October 2012 (UTC)

I confirm this, it is really exactly $=$, not $\approx$. Hanspi (talk) 21:22, 26 February 2014 (UTC)

sin(x)/x vs. sinc(x)

The article goes through the trouble of first introducing the sinc function, but then uses sin(x)/x instead of sinc(x) for all equations.

How about either dropping the introduction of sinc, or actually using it in the equations? Using it would be more consistent, since sin(x)/x isn't defined for x = 0. Moritz Lenz (talk) 08:23, 3 September 2018 (UTC)

Infinite products

I added a section "Infinite products", which covers two further spinoffs of the Borwein integrals. I know references for these facts:

Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, 2003.

Bailey, D. H.; Borwein, J. M.; Kapoor, V.; and Weisstein, E. W. "Ten Problems in Experimental Mathematics." Amer. Math. Monthly 113, 481-509, 2006.

Byron Schmuland, Random harmonic series, Amer. Math. Monthly 110 (2003), 407–416. http://www.stat.ualberta.ca/people/schmu/preprints/rhs.pdf

but when I tried to add them, the edit window crashed, probably because I was doing the formatting wrong. So if someone has the energy to put these in as proper references, I can link them up to the article correctly. Currently I just left them sitting there unformatted in the References section of the article.

Hi Prof.@John Baez. I added the references based on Wolfram's Infinite Cosine Product Integral page. I couldn't find exactly where you used the reference "Random harmonic series", so I added it to "Further reading". Please feel free to move it to where you find more adequate. I also couldn't find the citation for the "in fact Borwein and Bailey have shown" part. It is on Borwein and Bailey book? Cheers, Saung Tadashi (talk) 05:21, 10 January 2023 (UTC)

Possible typo

I'm an engineer not a mathematician (damnit) so am very hesitant about this, but in the equation after "At the next step the pattern fails" has a = been inadvertently replaced by a - ? MarkMLl (talk) 07:36, 23 November 2023 (UTC)

Odd. It looks like a (Firefox) rendering issue: both bars of the = are there but one appears to be rendered grey until one zooms in a long way. This behaviour is unchanged as the text is moved up and down the screen. MarkMLl (talk) 14:09, 24 November 2023 (UTC)