|
| |
|
|
A085565
|
|
Decimal expansion of lemniscate constant A.
|
|
6
| |
|
|
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; constant; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| This number is transcendental by a result of Schneider on elliptic integrals. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 08 2006
|
|
|
REFERENCES
| Th. Schneider, Transzendenzuntersuchungen periodischer Funktionen (1934).
Th. Schneider, Arithmetische Untersuchungen elliptischer Integrale (1937).
J. Todd, The lemniscate constants, Comm. ACM, 18 (1975), 14-19; 18 (1975), 462.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Lemniscate Constant
|
|
|
FORMULA
| (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.
Pi/sqrt(8)/agm(1,sqrt(1/2))
Pi/sqrt(8)*hypergeom([1/2,1/2],[1],1/2)
|
|
|
EXAMPLE
| 1.3110287771...
|
|
|
PROG
| (PARI) gamma(1/4)^2/4/sqrt(2*Pi)
|
|
|
CROSSREFS
| Cf. A076390.
Sequence in context: A072024 A011354 A143119 * A196057 A058395 A035694
Adjacent sequences: A085562 A085563 A085564 * A085566 A085567 A085568
|
|
|
KEYWORD
| nonn,cons
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 06 2003
|
| |
|
|
