[math-fun] first calculate 0.85250246642742 and then Google it
Yes, the wrong way round. But only after calculating the Statistical Process control parameters "d3" during 15 days, could I use the results to Google for it. I found that I wasn't the first to be frustrated by the 'generally accepted' 3-digit precision in SPC-tables like http://www.ct-yankee.com/spc/ and I wanted to know more, just like http://en.wikipedia.org/wiki/User:NorwegianBlue/refdesk/statistics Had I only found this site during my hours of Google-searching *before* doing the ugly double integral! Anyway, let's say that numerical accuracy to about 10 digits should suffice to uniquely make a floating point constant Googlable. Similar to what Simon Plouffe aspired with smaller hardware in his 'invertor'. http://bootes.math.uqam.ca/cgi-bin/ipcgi/lookup.pl?Submit=GO+&number=0.85250... Wouter. http://users.telenet.be/Wouter.Meeussen/Statistical%20Process%20Control%20d2...
Hello, I looked at your number in my tables : niet, I have 3.216 billions on disk here and 2.83 billion on static tables at the uqam site : nothing found. (I do have results but they are too far fetch to be considered). but... the identify function in Maple 13, found this :
identify(8.525024664, all); 1/2 7 3 ------ + 1/2 Zeta(3) + 9/5 exp(1) 4
ef(%); 8.52502465606
7/4*3^(1/2)+1/2*Zeta(3)+9/5*exp(1) well, if we play around with the Digits settings and the <all> option of that function then : arctan(-8/9*2^(1/2)+16/5*ln(2)+1/6*ln(3)) = 0.852502466428 What is the confortable precision of your result ? best regards, simon plouffe
Hi Simon, first of all, I use your site for such problems since years, and I appreciate it. I'm not so naive to expect a massive hit-rate. But it's a good place to try! As shown in the link at the bottom of my mail, I asked Mathematica for 20 significant digits, and got only 14 to 11. Only the last digit of 0.85250246642742 is in doubt with +/-1 as I understand Mma's precision indication: `nn.nn meaning 10^-nn.nn error. raw: {0.8525024664274217309882006698`13.9692, 0.8883680040452042872482772413`14.1417, 0.8798082028249833129922288768`13.5402, 0.8640819410995040789661639736`13.6221, 0.8480396861174952954262010116`13.2524, 0.8332053356222936613380562113`12.9727, 0.8198314897919439536038403347`12.7606, 0.8078342745533222767076702597`12.5445, 0.7970506735194112382518299112`12.402, 0.787314620550328268414227623`12.2977, 0.7784783412033843755984684354`12.0954, 0.7704162020637548294414698891`11.9747, 0.7630230956247903221251533661`11.9481, 0.7562114297279429899993948093`11.976, 0.7499080894099158663697529327`12.1145, 0.7440517839607317196049932255`11.8653, 0.738590853378178395574837`11.6318, 0.733481495518862923592541`11.4823, 0.728686345707299791511721`11.4005, 0.724173340717493263815453`11.3497, 0.719914808434216558974928`11.329, 0.715886735491807368853375`11.3405, 0.712068175147929010230738`11.3654, 0.708440765888656530842153`11.4463} Your suggestion evaluates to N[ArcTan[-8/9*2^(1/2)+16/5*Log[2]+1/6*Log[3]],24] 0.852502466428275502915601 to be compared to 0.85250246642742 and that's too far off. And I want to add a thanks to Eric http://mathworld.wolfram.com/StatisticalRange.html for setting me off on the right track. Wouter. ----- Original Message ----- From: "Simon Plouffe" <simon.plouffe@gmail.com> To: <math-fun@mailman.xmission.com> Sent: Saturday, February 20, 2010 4:50 PM Subject: Re: [math-fun] first calculate 0.85250246642742 and then Google it
Hello, I looked at your number in my tables : niet, I have 3.216 billions on disk here and 2.83 billion on static tables at the uqam site : nothing found.
(I do have results but they are too far fetch to be considered).
but... the identify function in Maple 13, found this :
identify(8.525024664, all); 1/2 7 3 ------ + 1/2 Zeta(3) + 9/5 exp(1) 4
ef(%); 8.52502465606
7/4*3^(1/2)+1/2*Zeta(3)+9/5*exp(1)
well,
if we play around with the Digits settings and the <all> option of that function then :
arctan(-8/9*2^(1/2)+16/5*ln(2)+1/6*ln(3)) = 0.852502466428
What is the confortable precision of your result ?
best regards,
simon plouffe
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