Complementary Modulus
If k is the elliptic modulus of an elliptic integral or elliptic function, then
| k^'=sqrt(1-k^2) |
(1)
|
is called the complementary modulus. Complete elliptic integrals with respect to the complementary modulus are often denoted
| K^'(k)=K(k^')=K(sqrt(1-k^2)) |
(2)
|
and
| E^'(k)=E(k^')=E(sqrt(1-k^2)). |
(3)
|
See also
Elliptic ModulusExplore with Wolfram|Alpha
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References
Tölke, F. "Parameterfunktionen." Ch. 3 in Praktische Funktionenlehre, zweiter Band: Theta-Funktionen und spezielle Weierstraßsche Funktionen. Berlin: Springer-Verlag, pp. 83-115, 1966.Referenced on Wolfram|Alpha
Complementary ModulusCite this as:
Weisstein, Eric W. "Complementary Modulus." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComplementaryModulus.html