Càlcul d’integrals usant sistemes dinàmics discrets

Authors

  • Armengol Gasull i Embid
  • Mireia Llorens

Abstract

If for a family of defined integrals, depending on parameters, the value of the integral remains unchanged when the values of the parameters vary in some special way, it is said that this change of parameters is a Landen transformation. Analogously, using dynamical systems terminology, this defined integral is a first integral of the discrete dynamical system associated with the Landen transformation. These transformations exist, for instance, for some families of elliptic integrals or for certain rational integrals. In this paper we present several examples of Landen transformations and we apply them to the computation of defined integrals. We also recall the Brent-Salamin algorithm for computing p, because it is based on these types of transformations. As we will see, the global dynamics of certain Landen transformations are far from being fully understood.

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Published

2017-07-11

How to Cite

Gasull i Embid, A., & Llorens, M. (2017). Càlcul d’integrals usant sistemes dinàmics discrets. Butlletí De La Societat Catalana De Matemàtiques, 32(1), 45–71. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/96509.004

Issue

Vol. 32 No. 1 (2017)

Section

Articles

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