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Complementary Parameter


The complementary parameter m^' associated with an elliptic parameter m is

 m^'=1-m.

If m=k^2, where k is the elliptic modulus, then m^'=(k^')^2, where k^' is the complementary modulus. Thus the complementary parameter is the square of the complementary modulus, rather than the complementary modulus itself (Abramowitz and Stegun 1972, p. 590). The prime denotes complementation, not a derivative. Abramowitz and Stegun use m_1 for the complementary parameter.


See also

Complementary Modulus, Elliptic Modulus, Elliptic Parameter

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References

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.

Cite this as:

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

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