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A closed solution to a special polynomial trinomial equation and semi-analytical roots for a general algebraic equation
- Publication Year :
- 2022
-
Abstract
- We suggest a closed solution for the roots of polynomial trinomial algebraic equation $$z^n+xz^{n-1}-1=0$$ with an appropriate $x$. This solution is a minor modification to the work of Mikhalkin (Mikhalkin E N, 2006. On solving general algebraic equations by integrals of elementary functions, Siberian Mathematical Jounral, 47(2), 301-306). This modification, together with Mikhalkin's integral formula, provides a relatively simple analytical expression for the solution to a general algebraic equation when the polynomial coefficients are over the corresponding convergent domain. Numerical examples show that this expression can be another alternative to finding numerically the roots of a general polynomial algebraic equation when the integral involved exists and is calculated correctly.<br />Comment: 14 pages, 7 figures, 1 table
- Subjects :
- Mathematics - General Mathematics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2205.04245
- Document Type :
- Working Paper