A064582 Real half-period for the Weierstrass elliptic function with invariants g2=0, g3=1.

1, 5, 2, 9, 9, 5, 4, 0, 3, 7, 0, 5, 7, 1, 9, 2, 8, 7, 4, 9, 1, 3, 1, 9, 4, 1, 7, 2, 3, 0, 8, 8, 2, 4, 3, 5, 8, 5, 7, 2, 8, 2, 8, 9, 4, 7, 1, 6, 0, 9, 2, 9, 4, 9, 6, 0, 6, 1, 8, 1, 1, 6, 8, 5, 9, 0, 9, 5, 2, 2, 3, 6, 1, 7, 9, 9, 3, 7, 4, 2, 7, 6, 4, 6, 8, 8, 3, 8, 5, 2, 0, 5, 6, 5, 8, 7, 5, 3, 4, 4, 6, 5

Offset

1,2

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 652.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.1.1 Weierstrass Pe Function, p. 422.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 652.

Amrik Singh Nimbran, Infinite series for omega-2 constant, 2020.

Simon Plouffe, Link to Simon Plouffe's Inverter.

Eric Weisstein's World of Mathematics, Omega-2 Constant.

Formula

Equals Gamma(1/3)^3/(4*Pi).

Also equals 2*2^(1/3)*EllipticK(4*sqrt(3)-7)/(135+78*sqrt(3))^(1/6). - Jean-François Alcover, Jun 18 2014

Example

1.5299540370571928749131941723...

Maple

s:= convert(evalf(GAMMA(1/3)^3/(4*Pi)/10, 140), string):
seq(parse(s[i+1]), i=1..104);  # Alois P. Heinz, Jun 18 2014

Mathematica

First@RealDigits[ Chop[ First@N[ WeierstrassHalfPeriods[ {0, 1} ], 102 ] ] ]
RealDigits[Gamma[1/3]^3/(4 Pi), 10, 100][[1]] (* Jan Mangaldan, Jan 06 2017 *)

Prog

(PARI) gamma(1/3)^3/4/Pi \\ Charles R Greathouse IV, Apr 18 2016
(Magma) C<i> := ComplexField(); [Gamma(1/3)^3/(4*Pi(C))]; // G. C. Greubel, Nov 05 2017

Crossrefs

Sequence in context: A255899 A348408 A019841 * A197374 A119946 A276610

Adjacent sequences: A064579 A064580 A064581 * A064583 A064584 A064585

Keyword

nonn,easy,cons

Author

Eric W. Weisstein, Sep 22 2001

Status

approved