Landen's Formula
where theta_i are Jacobi theta functions. This transformation was used by Gauss to show that elliptic integrals could be computed using the arithmetic-geometric mean.
See also
Jacobi Theta FunctionsExplore with Wolfram|Alpha
WolframAlpha
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Cite this as:
Weisstein, Eric W. "Landen's Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LandensFormula.html