English

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

General Mathematics 2024-06-11 v2

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\tan(x) - x = a was proved. This work applies the same topological method to prove the insolvability of equation xx=ax^x = a.

Cite

@article{arxiv.2312.02174,
  title  = {Insolvability of $x^x = a$ in elementary functions},
  author = {Alexey Kanel-Belov and Rodion Zaytsev},
  journal= {arXiv preprint arXiv:2312.02174},
  year   = {2024}
}

Comments

6 pages

R2 v1 2026-06-28T13:40:47.058Z