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Elliptic Argument

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Given a Jacobi amplitude phi in an elliptic integral, the argument u is defined by the relation

phi=am(u,k).

It is related to the elliptic integral of the first kind F(u,k) by

F(am(u,k),k)=u

(Abramowitz and Stegun 1972, p. 589).

See also

Elliptic Integral, Elliptic Integral of the First Kind, Jacobi Amplitude

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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, pp. 589-590, 1972.

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Elliptic Argument

Cite this as:

Weisstein, Eric W. "Elliptic Argument." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EllipticArgument.html

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