The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences

Efe Gürel

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arXiv · 2504.12697

The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences

Efe Gürel

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Abstract

In this paper, we expand the theory of Weierstrassian elliptic functions by introducing auxiliary zeta functions $\zeta_\lambda$, zeta differences of first kind $\Delta_\lambda$ and second kind $\Delta_{\lambda,\mu}$ where $\lambda,\mu=1,2,3$. Fundamental and novel results pertaining to these functions are proven. Furthermore, results already existing in the literature are translated in terms of auxiliary zeta functions. Their relationship to Jacobian elliptic functions and Jacobian functions are given.

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Efe Gürel. 2025-04-17. The Theory Of Auxiliary Weierstrassian Zeta Functions And Zeta Differences. https://arxiv.org/abs/2504.12697

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