What is the mathematical meaning of this symbol? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-23T03:43:23Z http://mathoverflow.net/feeds/question/22266 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22266/what-is-the-mathematical-meaning-of-this-symbol What is the mathematical meaning of this symbol? fuzzylintman 2010-04-22T22:01:49Z 2013-02-19T15:20:14Z <p>Someone asked me, and I told them I would try to find out... what is the meaning of this symbol:</p> <p>B'<sub>L</sub> &nbsp; &nbsp; or &nbsp; &nbsp; B<sub>L</sub>'</p> <p>(I'm not sure if the tick comes before or after the L. It was found on a "nerd clock". The value of this symbol, by the way, is 1.</p> http://mathoverflow.net/questions/22266/what-is-the-mathematical-meaning-of-this-symbol/22268#22268 Answer by Mariano Suárez-Alvarez for What is the mathematical meaning of this symbol? Mariano Suárez-Alvarez 2010-04-22T22:10:14Z 2010-04-22T22:10:14Z <p>Apparently, it is supposed to be <a href="http://en.wikipedia.org/wiki/Legendre%27s_constant" rel="nofollow">Legendre's constant</a>, also known as $1$.</p> http://mathoverflow.net/questions/22266/what-is-the-mathematical-meaning-of-this-symbol/22293#22293 Answer by Álvaro Lozano-Robledo for What is the mathematical meaning of this symbol? Álvaro Lozano-Robledo 2010-04-23T02:59:29Z 2010-04-23T02:59:29Z <p>Hi,</p> <p>This was supposed to be a comment to Mariano's answer, but it seems too long for a comment.</p> <p>Somebody gave me <a href="http://www.photodump.com/wp-content/uploads/2009/09/geek-clock.jpg" rel="nofollow">that clock</a> for Christmas and all along I thought $B_L'=1$ was some silly Physics constant... but it seems Mariano is right, and this refers to Legendre's constant (at least, that's the case according to <a href="http://docs.google.com/View?docid=dcxsck6d_29dc8q3nf5" rel="nofollow">this other site</a>). </p> <p>I was terribly curious, though, to find out where this notation came from and decided to go right to the source, "Essai sur la Theorie des Nombres", by Legendre. Amazingly, our friends at Google have scanned the whole book, and the whole volume is <a href="http://books.google.com/books?id=ZHYAAAAAMAAJ&amp;printsec=frontcover&amp;dq=legendre+theorie+des+nombres&amp;cd=3#v=onepage&amp;q&amp;f=false" rel="nofollow">freely available here</a>. It is a large volume, however! So it was not easy to locate the exact place where Legendre talks about the prime counting function. A nice paper by Goldstein in the American Math Monthly, <a href="http://www.jstor.org/pss/2319162" rel="nofollow">"A history of the prime number theorem"</a>" was very helpful to locate the exact reference: <strong>p. 394-398 in the second edition</strong> of the "Essai sur..." by Legendre.</p> <p>In p. 395, Legendre explains that $\pi(x)$, the number of primes $\leq x$, seems to grow like $$\frac{x}{A\log x + B}$$ and conjectures that $A=1$ and $B=-1.08366\ldots$ (now a famous mistake, since later on the proofs of the prime number theorem would show that $B=1$). But, in any case, Legendre himself called this constant $B$ and I suppose somebody added the subscript $L$, to $B_L$, to remind us of Legendre's name. </p> <p>However, I am still puzzled by the apostrophe, $B_L'$.</p> http://mathoverflow.net/questions/22266/what-is-the-mathematical-meaning-of-this-symbol/122313#122313 Answer by Smac for What is the mathematical meaning of this symbol? Smac 2013-02-19T15:20:14Z 2013-02-19T15:20:14Z <p>I think it is B'L. It could mean that B, as suggested above, does equal 1 and the ' can mean possession. Like Joe's car means the car of Joe, B'L means the constant of Legendre. Just a thought.</p>