OFFSET
-1,2
COMMENTS
The Pearson correlation coefficient where the maximum difference occurs is given by A228402.
LINKS
Iain Fox, Table of n, a(n) for n = -1..20000
C. Croux and C. Dehon, Influence functions of the Spearman and Kendall correlation measures, Statistical Methods and Applications, 19(4), 497-515, 2010, (see Eq. 5).
R. Guérin, J. C. de Oliveira, and S. Weber, Adoption of bundled services with network externalities and correlated affinities, arXiv:1310.4429 [cs.NI], 2013.
FORMULA
2*sqrt((Pi-3)*(Pi+3))/Pi - 6/Pi*arcsin((2*sqrt((Pi-3)*(Pi+3))/Pi)/2).
EXAMPLE
0.018083177430872294003006565434951459128139228361067...
MATHEMATICA
c = Sqrt[4*Pi^2 - 36]/Pi; RealDigits[c - 6/Pi*ArcSin[c/2], 10, 110] (* T. D. Noe, Nov 04 2013 *)
PROG
(MATLAB) vpa('2*((pi-3)*(pi+3))^.5/pi-6/pi*asin( (2*((pi-3)*(pi+3))^.5/pi)/2)', 50)
(PARI) 2*sqrt((Pi-3)*(Pi+3))/Pi - 6/Pi*asin((2*sqrt((Pi-3)*(Pi+3))/Pi)/2) \\ Michel Marcus, Dec 17 2017
(PARI) { default(realprecision, 20080); x=100*(2*sqrt((Pi-3)*(Pi+3))/Pi - 6/Pi*asin((2*sqrt((Pi-3)*(Pi+3))/Pi)/2)); for (n=-1, 20000, d=floor(x); x=(x-d)*10; write("b228438.txt", n, " ", d)); } \\ Iain Fox, Dec 17 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Joost de Winter, Nov 02 2013
STATUS
approved