论文标题
landen施用用于近似
Landen transformations applied to approximation
论文作者
论文摘要
我们研究了在几何函数理论和准形式映射理论中复发特殊功能近似的计算方法。所研究的功能可以表示为完整的椭圆积分的商和此类商的倒置。特别是，我们考虑$ | f（x）| $ f（x）| $时的失真函数$ f（x）| $时，当$ f：\ mathbb {b}^2 \ to \ mathbb {b}^2，f（f（0）= 0，$是单位磁盘$ \ mathbb {b mathbb {b} beftion of the of the of the of the of the of the of the of。 Landen迭代足以达到机器精度。
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 $φ_K(r)$ which gives a majorant for $|f(x)|$ when $f: \mathbb{B}^2 \to \mathbb{B}^2, f(0)=0,$ is a quasiconformal mapping of the unit disk $\mathbb{B}^2.$ It turns out that the approximation method is very simple: five steps of Landen iteration is enough to achieve machine precision.
