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Search: id:A014549
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| A014549 |
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Decimal expansion of 1 / M(1,sqrt(2)) (Gauss's constant). |
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+0
7
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| 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
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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On May 30, 1799, Gauss discovered that this number is also equal to (2/Pi)*Integral(1/sqrt(1-t^4),t=0..1).
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).
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REFERENCES
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J. M. Borwein and P. B. Borwein, Pi and the AGM, page 5.
J. R. Goldman, The Queen of Mathematics, 1998, p. 92.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean
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EXAMPLE
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0.8346268416740731862814297327990468...
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PROGRAM
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(PARI) { default(realprecision, 20080); x=10*agm(1, sqrt(2))^-1; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b014549.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 20 2009]
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CROSSREFS
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Cf. A053002, A053003, A053004.
Sequence in context: A070597 A091895 A111436 this_sequence A021549 A013665 A110234
Adjacent sequences: A014546 A014547 A014548 this_sequence A014550 A014551 A014552
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KEYWORD
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nonn,cons,nice
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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