Applied Mathematics & Physics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Applied Mathematics & Physics:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Applied Mathematics & Physics, 2021, Volume 53, Issue 3, Pages 230–234
DOI: https://doi.org/10.52575/2687-0959-2021-53-3-230-234
(Mi pmf314)
 

MATHEMATICS

Hypergeometric interpretation of the Descartes-Euler formula to solve the fourth degree equation

E. N. Mikhalkin

Siberian Federal University
Abstract: 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.
Keywords: Algebraic equation. Hypergeometric series. Mellin-Barnes integral.
Received: 30.09.2021
Document Type: Article
Language: Russian
Linking options:
  • https://www.mathnet.ru/eng/pmf314
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Applied Mathematics & Physics
    Statistics & downloads:
    Abstract page:14
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025