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arXiv · 2202.10306

Real-Analyticity of Generalized Sine Functions with Two Parameters

Pisheng Ding
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Abstract

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 $(1/2){\pi}_{p,n}$ iff $p=m/(m-1)$ for some integer $m>1$, in which case we determine the radius of convergence of the Taylor series at $(1/2){\pi}_{p,n}$.

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Pisheng Ding. 2022-02-21. Real-Analyticity of Generalized Sine Functions with Two Parameters. https://doi.org/10.1007/s41478-022-00493-z

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