HYPERGEOMETRIC INTERPRETATION OF THE DESCARTES-EULER FORMULA TO SOLVE THE FOURTH DEGREE EQUATION
DOI:
https://doi.org/10.52575/2687-0959-2021-53-3-230–234Keywords:
Algebraic equation. Hypergeometric series. Mellin-Barnes integralAbstract
In modern mathematics by development of algorithmic and computer methods formulas for solving polynomial equations are considered in more details. In the paper a polynomial equation of fourth power with one parameter is considered.
Such equations are called trinomial. For it such methods of solution are known as methods of Ferrari, Descartes and Euler. An approach is used based on Mellin and Belardinelli integral representations, and also usage of the inverse Mellin transform.
As a main result the formula is proved for solutions obtained by Euler – Descartes method with representations of series for hypergeometric functions.
Downloads
References
Бейтмен Г., Эрдейи А. 1973. Высшие трансцендентные функции, Том 1. М., Наука, 296.
Корн Г., Корн Т. 2003. Справочник по математике для научных работников и инженеров. СПб, Лань, 832.
Курош А.Г. 2021. Курс высшей алгебры. СПб., Лань, 432.
Михалкин Е. Н. 2012. Некоторые формулы для решений триномиальных и тетраномиальных алгебраических уравнений. Журнал СФУ. Сер. Матем. и физ., 5(2): 230–238.
Belardinelli G. 1960. Fonctions hyperg'eom'etriques de plusieurs variables et resolution analytique des equations algebrigues generales. Paris: Gauthier-Villars. Memorial des Sciences Mathematiques, 74.
Mellin H.J. 1921. Resolution de l`equation algebrique generale alaide de la fonction gamma. C. R. Acad. Sci. Paris Ser. I Math., 172: 658-661.
Abstract views: 229
##submission.share##
Published
Versions
- 2021-09-30 (2)
- 2021-09-30 (1)
How to Cite
Issue
Section
Copyright (c) 2021 Applied Mathematics & Physics
This work is licensed under a Creative Commons Attribution 4.0 International License.
