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Search: id:A085565
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| A085565 |
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Decimal expansion of lemniscate constant A. |
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+0
2
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| 1, 3, 1, 1, 0, 2, 8, 7, 7, 7, 1, 4, 6, 0, 5, 9, 9, 0, 5, 2, 3, 2, 4, 1, 9, 7, 9, 4, 9, 4, 5, 5, 5, 9, 7, 0, 6, 8, 4, 1, 3, 7, 7, 4, 7, 5, 7, 1, 5, 8, 1, 1, 5, 8, 1, 4, 0, 8, 4, 1, 0, 8, 5, 1, 9, 0, 0, 3, 9, 5, 2, 9, 3, 5, 3, 5, 2, 0, 7, 1, 2, 5, 1, 1, 5, 1, 4, 7, 7, 6, 6, 4, 8, 0, 7, 1, 4, 5, 4
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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This number is transcendental by a result of Schneider on elliptic integrals. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 08 2006
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REFERENCES
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J. Todd, The lemniscate constants, Comm. ACM, 18 (1975), 14-19; 18 (1975), 462.
Th. Schneider, Transzendenzuntersuchungen periodischer Funktionen (1934).
Th. Schneider, Arithmetische Untersuchungen elliptischer Integrale (1937).
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LINKS
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Eric Weisstein's World of Mathematics, Lemniscate Constant
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FORMULA
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(1/4)*(2*Pi)^(-1/2)*GAMMA(1/4)^2.
Integral_{1}^{infty}dx/sqrt(4x^3-4x)=Gamma(1/4)^2/4/sqrt(2*Pi)=1.31102877714605990523.... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 08 2006
Equals product (k=0, infinity, [(4k+3)(4k+2)] / [(4k+5)(4k+4)] ) (Gauss). - R. Stephan, Mar 04, 2008.
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EXAMPLE
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1.3110287771...
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PROGRAM
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(PARI) gamma(1/4)^2/4/sqrt(2*Pi)
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CROSSREFS
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Cf. A085566.
Adjacent sequences: A085562 A085563 A085564 this_sequence A085566 A085567 A085568
Sequence in context: A072024 A011354 A143119 this_sequence A058395 A035694 A006941
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KEYWORD
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nonn,cons
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AUTHOR
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njas, Jul 06 2003
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