论文标题
具有两个参数的广义正弦函数的实现分析
Real-Analyticity of Generalized Sine Functions with Two Parameters
论文作者
论文摘要
我们确定$ \ sin_ {p，n} $在任何实际数字$ p> 1 $和任何整数$ n> 1 $的最大真实间隔。我们首先证明$ \ sin_ {p，n} $在$（1/2）π_{p，n} $ iff $ p = m/（m-1）$中，对于某些整数$ m> 1 $，在这种情况下，我们确定泰勒convergence系列的半径为$（1/2）$（1/2）π__{p，n}。
We identify the maximal real interval on which $\sin_{p,n}$ is real-analytic for any real number $p>1$ and any integer $n>1$. We achieve this by first proving that $\sin_{p,n}$ is analytic at $(1/2)π_{p,n}$ iff $p=m/(m-1)$ for some integer $m>1$, in which case we determine the radius of convergence of the Taylor series at $(1/2)π_{p,n}$.
