omega_2 Constant

In the equianharmonic case of the Weierstrass elliptic function, corresponding to invariants g_2=0 and g_3=1, the corresponding real half-period is given by


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


(OEIS A094961 and A094962).

See also

Equianharmonic Case, Half-Period, Omega Constant, Weierstrass Constant, Weierstrass Elliptic Function

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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. "omega_2 Constant." From MathWorld--A Wolfram Web Resource.

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