Landen transformations and the integration of rational functions

Boros, George; Moll, Victor

doi:10.1090/S0025-5718-01-01347-3

Landen transformations and the integration of rational functions
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by George Boros and Victor H. Moll PDF

Math. Comp. 71 (2002), 649-668 Request permission

Abstract:

We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closed-form expressions for a large class of integrals of even rational functions and to develop an algorithm for numerical integration of these functions.

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