Insolvability of $x^x = a$ in elementary functions

Alexey Kanel-Belov; Rodion Zaytsev

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arXiv · 2312.02174

Insolvability of $x^x = a$ in elementary functions

Alexey Kanel-Belov·Rodion Zaytsev

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Abstract

In a recent paper "Solvability of equations in elementary functions" [arXiv:1911.10409] the insolvability in elementary functions of equation $\tan(x) - x = a$ was proved. This work applies the same topological method to prove the insolvability of equation $x^x = a$.

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BibTeX RIS

Alexey Kanel-Belov, Rodion Zaytsev. 2023-11-05. Insolvability of $x^x = a$ in elementary functions. https://arxiv.org/abs/2312.02174

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