OFFSET
0,2
COMMENTS
M(a,b) is the limit of the arithmetic-geometric mean iteration applied repeatedly starting with a and b: a_0=a, b_0=b, a_{n+1}=(a_n+b_n)/2, b_{n+1}=sqrt(a_n*b_n).
REFERENCES
J. M. Borwein and P. B. Borwein, Pi and the AGM, page 5.
J. R. Goldman, The Queen of Mathematics, 1998, p. 92.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..19999
Eric Weisstein's World of Mathematics, Gauss's Constant.
G. Xiao, Contfrac
EXAMPLE
1.19814023473559220743992249228...
MATHEMATICA
ContinuedFraction[ArithmeticGeometricMean[1, Sqrt[2]], 100] (* Harvey P. Dale, Feb 26 2012 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(agm(1, sqrt(2))); for (n=1, 20000, write("b053003.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 20 2009
CROSSREFS
KEYWORD
nonn,cofr,nice,easy
AUTHOR
N. J. A. Sloane, Feb 21 2000
EXTENSIONS
More terms from James A. Sellers, Feb 22 2000
Offset changed by Andrew Howroyd, Aug 03 2024
STATUS
approved