APPLICATIONS OF EULERIAN INTEGRALS
Keywords:
beta function, gamma function, eulerian integrals, elliptic functions, modeling of phenomena, Bessel functions, elliptic differential equationsAbstract
This article is devoted to eulerian integrals of the first and second kind, also known as gamma and beta functions, which are widely used in various fields of mathematics and physics. This article discusses the main properties of these integrals and their application in science, and also discusses specific problems that can be solved using eulerian integrals of the first and second kind. Note that the use of eulerian integrals can significantly simplify the calculation of certain integrals, including improper ones. And also to solve the problem in the event that for a subintegral function, the primitive cannot be found in the final form. Due to their properties, eulerian integrals of the first and second kind are a powerful tool for analyzing and solving various mathematical and physical problems. Therefore, the study of the properties of eulerian integrals is useful to anyone who is interested in mathematics and the possibilities of using them not only in mathematics, but also in solving applied problems.
References
Виленкин, Н.Я., Куницкая, Е.С, Мордкович, А.Г. Математический анализ: интегральное исчисление. М.: Наука, 1979. – 435 с.
Фихтенгольц, Г.М. Курс дифференциального и интегрального исчисления. Т. 2. М.: Физматгиз, 1962. – 807 с.
Гусак, А.А. Высшая математика. Учебник для студентов вузов. В 2 т. – том 1, 6-е изд. – Минск: ТетраСистемс, 2010. – 544 с.
Кошляков, Н.С., Глинер Э.Б., Смирнов М.М. Основные дифференциальные уравнения математической физики. - М.: Физматгиз, 1962. — 710 с..
Лебедев, Н. Н. Специальные функции и их приложения - М.: Гостехиздат, 1963. ¬– 377 с.
Функции Бесселя: Учебно-методическое пособие / Сост.: В.И.Зубов. – М.: МФТИ, 2007. – 51 с.
