%I #14 Jun 20 2017 22:50:45

%S 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,

%T 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,7,5,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,4,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9

%N Decimal expansion of AGM(1-x,1+x), where x=1/(10^27+1).

%C 0.999999999...9999999999750000000...000004999999...9999991718750000000...000001312499... (see the first link).

%H Gerd Lamprecht, <a href="http://www.gerdlamprecht.de/AlmostInteger.htm">Almost Integer, Patterns in decimals</a>

%H Gerd Lamprecht, <a href="http://pi.gerdlamprecht.de/"> 10000 digit from A-646 in pi.gerdlamprecht.de database</a>

%F Equals Pi/(2*K(1/(10^27+1)^2)), where K is the complete elliptic integral of the first kind. - _Bruno Berselli_, Mar 07 2013

%e 0.99999999999999999999999999999999999999999999999999999975000000000000...

%o (PARI) x=1/(10^27+1); agm(1-x,1+x) \\ _Charles R Greathouse IV_, Mar 03 2016

%o (PARI) agm(sqrt(1-1/(10^27+1)^2),1) \\ _Charles R Greathouse IV_, Mar 03 2016

%K cons,nonn,less

%O 0,1

%A Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Nov 05 2010