2021/12/11 by Raghavendra G. Kulkarni, Kulkarni, Raghavendra G.
Engineering · Mathematics · Physics and Astronomy · #12E12 #Experimental and Theoretical Physics Studies #FOS: Mathematics #General Mathematics (math.GM) #Photonic and Optical Devices #math.GM #msc:12E12
paper · pdf · doi:10.48550/arxiv.2112.06021
10 pages, 3 tables
openalex publication_date 2021/12/11 · arxiv created 2021/12/29 · arxiv updated 2021/12/30 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In this paper, we propose a new method to obtain a solution to a single-parameter Bring quintic equation of the form, x5+x=a, where a is real. The method transforms the given quintic equation to an infinite but convergent series expression in (x/a), which is further transformed to a quartic equation in a novel fashion. The coefficients of the quartic equation so obtained are some kind of infinite series expressions in a-4, which are termed as ultraradicals. The quartic equation is then solved and its one real solution is picked; further using this, the real solution of quintic equation, x5+x=a, is extracted. The ultraradicals used in this method converge for |a| > 1; hence the method can be used when |a| > 1.