

A014549


Decimal expansion of 1 / M(1,sqrt(2)) (Gauss's constant).


10



8, 3, 4, 6, 2, 6, 8, 4, 1, 6, 7, 4, 0, 7, 3, 1, 8, 6, 2, 8, 1, 4, 2, 9, 7, 3, 2, 7, 9, 9, 0, 4, 6, 8, 0, 8, 9, 9, 3, 9, 9, 3, 0, 1, 3, 4, 9, 0, 3, 4, 7, 0, 0, 2, 4, 4, 9, 8, 2, 7, 3, 7, 0, 1, 0, 3, 6, 8, 1, 9, 9, 2, 7, 0, 9, 5, 2, 6, 4, 1, 1, 8, 6, 9, 6, 9, 1, 1, 6, 0, 3, 5, 1, 2, 7, 5, 3, 2, 4, 1, 2, 9, 0, 6, 8
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OFFSET

0,1


COMMENTS

On May 30, 1799, Gauss discovered that this number is also equal to (2/Pi)*Integral(1/sqrt(1t^4),t=0..1).
M(a,b) is the limit of the arithmeticgeometric 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,...,20000
Eric Weisstein's World of Mathematics, Gauss's Constant
Eric Weisstein's World of Mathematics, ArithmeticGeometric Mean


EXAMPLE

0.8346268416740731862814297327990468...


MATHEMATICA

RealDigits[ N[ Gamma[1/4]^2/(2*Pi^(3/2)*Sqrt[2]), 105]][[1]] (* JeanFrançois Alcover, Dec 13 2011, after Eric Weisstein *)


PROG

(PARI) { default(realprecision, 20080); x=10*agm(1, sqrt(2))^1; for (n=0, 20000, d=floor(x); x=(xd)*10; write("b014549.txt", n, " ", d)); } [From Harry J. Smith, Apr 20 2009]


CROSSREFS

Cf. A053002, A053003, A053004.
Sequence in context: A222232 A091895 A111436 * A021549 A013665 A209059
Adjacent sequences: A014546 A014547 A014548 * A014550 A014551 A014552


KEYWORD

nonn,cons,nice


AUTHOR

Eric W. Weisstein, N. J. A. Sloane.


EXTENSIONS

Fixed my PARI program, had n Harry J. Smith, May 19 2009
Extended at 105 terms by JeanFrançois Alcover, Dec 13 2011


STATUS

approved



