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arXiv · 2201.07414

Generalized Sine Functions, Complexified

Pisheng Ding·Sunil K. Chebolu
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Abstract

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.

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Pisheng Ding, Sunil K. Chebolu. 2022-01-19. Generalized Sine Functions, Complexified. https://arxiv.org/abs/2201.07414

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