The case of the Weierstrass elliptic function with invariants 
and 
. In this case, the half-periods
are given by 
,
where 
is 
times the lemniscate constant,
 |  |  |
(1)
|
 |  | ![([Gamma(1/4)]^2)/(4sqrt(pi))](/images/equations/LemniscateCase/Inline11.svg) |
(2)
|
 |  |  |
(3)
|
(OEIS A093341; Abramowitz and Stegun 1972, p. 658).
Lemniscate Case
See also
Equianharmonic Case, Lemniscate Constant, Weierstrass Elliptic Function, Pseudolemniscate CaseExplore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). "Lemniscate Case (
,
)." §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 CaseCite this as:
Weisstein, Eric W. "Lemniscate Case." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LemniscateCase.html