Landen transformations applied to approximation




Kargar, Rahim; Rainio, Oona; Vuorinen, Matti

PublisherYokohama Publications

2024

Pure and Applied Functional Analysis

Pure and Applied Functional Analysis

9

2

503

516

2189-3756

https://arxiv.org/pdf/2212.09336(external)

https://arxiv.org/abs/2212.09336(external)



We study computational methods for the approximation of special functions recurrent in geometric function theory and quasiconformal mapping theory. The functions studied can be expressed as quotients of complete elliptic integrals and as inverses of such quotients. In particular, we consider the distortion function φk(r) which gives a majorant for |f(x)| when f: B2 → B2, f(0) = 0, is a quasiconformal mapping of the unit disk B2. It turns out that the approximation method is very simple: Five steps of Landen iteration are enough to achieve machine precision.



Last updated on 2025-27-01 at 19:34