A064582 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

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