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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 Modulus

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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.

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Complementary Modulus

Cite this as:

Weisstein, Eric W. "Complementary Modulus." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ComplementaryModulus.html

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