标题： 椭圆上面积积分的计数方法与第二类 Tchebychev 多项式 显示英文标题

标题： Counting methods of area integrals and Tchebychev polynomials of second kind on the ellipse

摘要： 我们利用Gronwall的面积公式来计算一些不同区域（如圆、椭圆和伯努利双纽线）的面积。我们使用从单位圆盘外部到这些区域之一的共形映射的Laurent级数和Taylor级数展开式来计算这些区域的面积。本文最后讨论了椭圆上的第二类Tchebychev正交多项式以及插值问题。 显示英文摘要

摘要： We use Gronwall's area formula to find the area of some differents regions as circles, ellipses and lemniscates.We use Laurent and Taylor series expansions of conformal mapping from the exterior of the unit disk to either of these regions to compute the area of them.We close this work with the discussion of orthogonal Tchebychev polynomials of second kind on the ellipse and interpolation.