In the equianharmonic case of the Weierstrass elliptic function, corresponding to invariants and , the corresponding real half-period is given by

			(1)
			(2)

(Sloane's A064582), where is the gamma function. The other half-period is then given by

			(3)
			(4)
			(5)

(Sloane's A094961 and A094962).

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 652-653, 1972.

Finch, S. R. "Gauss' Lemniscate Constant." §6.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 420-423, 2003.

Sloane, N. J. A. Sequences A064582, A094961, and A094962 in "The On-Line Encyclopedia of Integer Sequences."

CITE THIS AS:

Weisstein, Eric W. "omega2 Constant." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Omega-2Constant.html