论文标题
广义的正弦函数，复杂化
Generalized Sine Functions, Complexified
论文作者
论文摘要
广义的正弦和余弦函数，$ \ sin_ {n} $和$ \ cos_ {n} $，参数化通用的单位圆圈$ x^n+y^n = 1 $是，就像它们的经典圆形对应物一样，可作为复杂的分析功能扩展。在本文中，我们确定了$ \ sin_ {n} $的自然域，是从多边形到具有$ n $ slits的复杂平面的形式等价。我们还提供了一些几何和分析应用。
Generalized sine and cosine functions, $\sin_{n}$ and $\cos_{n}$, that parametrize the generalized unit circle $x^n+y^n=1$ are, much like their classical circular counterparts, extendable as complex analytic functions. In this article, we identify the natural domain on which $\sin_{n}$ is a conformal equivalence from a polygon to the complex plane with $n$ slits. We also give some geometric and analytic applications.
