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A062539 Decimal expansion of the Lemniscate constant or Gauss's constant. 15
2, 6, 2, 2, 0, 5, 7, 5, 5, 4, 2, 9, 2, 1, 1, 9, 8, 1, 0, 4, 6, 4, 8, 3, 9, 5, 8, 9, 8, 9, 1, 1, 1, 9, 4, 1, 3, 6, 8, 2, 7, 5, 4, 9, 5, 1, 4, 3, 1, 6, 2, 3, 1, 6, 2, 8, 1, 6, 8, 2, 1, 7, 0, 3, 8, 0, 0, 7, 9, 0, 5, 8, 7, 0, 7, 0, 4, 1, 4, 2, 5, 0, 2, 3, 0, 2, 9, 5, 5, 3, 2, 9, 6, 1, 4, 2, 9, 0, 9, 3, 4, 4, 6, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n=1..5000

Simon Plouffe, Lemniscate or Gauss constant

Simon Plouffe, Lemniscate constant or Gauss constant

Eric Weisstein's World of Mathematics, Lemniscate Constant

FORMULA

1/2*Pi^(3/2)/GAMMA(3/4)^2*2^(1/2).

A093341 multiplied by A002193. - R. J. Mathar, Aug 28 2013

EXAMPLE

2.622057554292119810464839589891119413682754951431623162816821703...

MATHEMATICA

RealDigits[Pi^(3/2)/Gamma[3/4]^2*2^(1/2)/2, 10, 111][[1]] (* Robert G. Wilson v, May 19 2004 *)

PROG

(PARI) print(1/2*Pi^(3/2)/gamma(3/4)^2*2^(1/2))

(PARI) allocatemem(932245000); default(realprecision, 5080); x=Pi^(3/2)*sqrt(2)/(2*gamma(3/4)^2); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b062539.txt", n, " ", d)); \\ Harry J. Smith, Jun 20 2009

(PARI) Pi/agm(1, sqrt(2)) \\ Charles R Greathouse IV, Feb 04 2015

CROSSREFS

Cf. A062540, A064853.

Sequence in context: A204935 A008905 A136760 * A171898 A110218 A057892

Adjacent sequences:  A062536 A062537 A062538 * A062540 A062541 A062542

KEYWORD

cons,easy,nonn

AUTHOR

Jason Earls (zevi_35711(AT)yahoo.com), Jun 25 2001

STATUS

approved

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Last modified August 27 17:19 EDT 2015. Contains 261095 sequences.