TOPICS
Search

Lemniscate Case

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook

The case of the Weierstrass elliptic function with invariants g_2=1 and g_3=0. In this case, the half-periods are given by (omega_1,omega_2)=(omega,iomega), where omega is 1/(2sqrt(2)) times the lemniscate constant,

omega=L/(2sqrt(2))
(1)
=([Gamma(1/4)]^2)/(4sqrt(pi))
(2)
=1.8540746...
(3)

(OEIS A093341; Abramowitz and Stegun 1972, p. 658).

See also

Equianharmonic Case, Lemniscate Constant, Weierstrass Elliptic Function, Pseudolemniscate Case

Explore with Wolfram|Alpha

References

Abramowitz, M. and Stegun, I. A. (Eds.). "Lemniscate Case (g_2=1, g_3=0)." §18.14 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 658-662, 1972.Sloane, N. J. A. Sequence A093341 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Lemniscate Case

Cite this as:

Weisstein, Eric W. "Lemniscate Case." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LemniscateCase.html

Subject classifications