Rational Landen transformations on ℝ

Manna, Dante; Moll, Victor

doi:10.1090/S0025-5718-07-01954-0

Rational Landen transformations on $\mathbb {R}$
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Math. Comp. 76 (2007), 2023-2043 Request permission

Abstract:

The Landen transformation $(a,b) \mapsto ( (a+b)/2,\sqrt {ab} )$ preserves the value of an elliptic integral, and its iteration produces the classical arithmetic-geometric mean $\text {AGM}(a,b)$. We present analogous transformations for rational functions integrated over the whole real line.

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