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 A062539 Decimal expansion of the Lemniscate constant or Gauss's constant. 16
 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 Equals (1/2)*sqrt(2*Pi^3)/Gamma(3/4)^2. A093341 multiplied by A002193. - R. J. Mathar, Aug 28 2013 From Martin Renner, Aug 16 2019: (Start) Equals 2*Integral_{x=0..1} 1/sqrt(1-x^4) dx. Equals 1/2*B(1/4,1/2) with Beta function B(x,y) = Gamma(x)*Gamma(y)/Gamma(x+y). (End) EXAMPLE 2.622057554292119810464839589891119413682754951431623162816821703... MAPLE evalf((1/2)*sqrt(2*Pi^3)/GAMMA(3/4)^2, 120); # Muniru A Asiru, Oct 08 2018 evalf(1/2*GAMMA(1/4)*GAMMA(1/2)/GAMMA(3/4), 120); # Martin Renner, Aug 16 2019 evalf(1/2*Beta(1/4, 1/2), 120); # Martin Renner, Aug 16 2019 evalf(2*int(1/sqrt(1-x^4), x=0..1), 120); # Martin Renner, Aug 16 2019 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 (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); (1/2)*Sqrt(2*Pi(R)^3)/Gamma(3/4)^2; // G. C. Greubel, Oct 07 2018 CROSSREFS Cf. A062540, A064853. Cf. A002193, A093341. Equals A000796/A053004 (see PARI script). Sequence in context: A303335 A332390 A289382 * A064136 A171898 A330541 Adjacent sequences:  A062536 A062537 A062538 * A062540 A062541 A062542 KEYWORD cons,easy,nonn AUTHOR Jason Earls, Jun 25 2001 STATUS approved

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Last modified October 24 07:04 EDT 2020. Contains 337975 sequences. (Running on oeis4.)