omega_2 Constant

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

			(1)
			(2)

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

			(3)
			(4)
			(5)

(OEIS A094961 and A094962).

REFERENCES:

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."