Rational Landen Transformations on R Dante Manna and Victor

نویسندگان

H. MOLL

VICTOR H. MOLL

چکیده

The Landen transformation (a, b) 7→ ((a+b)/2, √ ab) preserves the value of an elliptic integral and its iteration produces the classical arithmeticgeometric mean AGM(a, b). We present analogous transformations for rational functions integrated over the whole real line.

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The Landen transformation (a, b) → ((a+b)/2, √ ab) preserves the value of an elliptic integral, and its iteration produces the classical arithmeticgeometric mean AGM(a, b). We present analogous transformations for rational functions integrated over the whole real line.

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