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.
