Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Adamchik V.S., Marichev O.I. — The algorithm for calculating integrals of hypergeometric type functions and its realization in reduce system
Adamchik   V.S., Marichev O.I. — The algorithm for calculating integrals of hypergeometric type functions and its realization in reduce system

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: The algorithm for calculating integrals of hypergeometric type functions and its realization in reduce system

Авторы: Adamchik V.S., Marichev O.I.

Аннотация:

The most voluminous bibliography of the analytical methods for calculating of integrals is represented in the article [19]. It is shown there that the most effective and the simplest algorithm of analytical integration was made by O.I. Marichev [8, 9, 12]. Later it was realized in the reference-books [16-18, 20]. This algorithm allows us to calculate definite and indefinite integrals of the products of elementary and special functions of hypergeometric type. It embraces about 70 per cent of integrals which are included in the world reference-literature. It allows to calculate many other integrals too. The present article contains short description of this algorithm and its realization in the REDUCE system during the process of creation of INTEGRATOR system. Only one general method of integration is known to be realized on the computers, i.e. criterion algorithm for calculating of indefinite integrals of elementary functions through elementary functions by themselves (the authors of it are M. Bronstein and other). The idea of our algorithm is in the following. The initial integrals is transformed to contour integral from the ratio of products of gamma-functions by means of Mellin transform and parseval equality. The residue theorem is used for the calculating of the received integral which due to the strict rules results in sums of hypergeometric series. The value of integral itself and the integrand functions are the special cases of the well-known Meijer's G-function [4, 7, 8, 12, 14, 18]. Programming packet is realized in programming languages PASCAL and REDUCE. It also offers the opportunity of finding the values for some classical integral transforms (Laplace, Hankel, Fourier, Mellin and etc.). The REDUCE's part of packet contains the main properties of the well-known special functions, such as the Bessel and gamma-functions and kindred functions, Anger function, Weber function, Whittaker functions, generalized hypergeometric functions. Special place in the packet is occupied by Meijers's G-function for which the main properties such as finding the particular cases and representation by means of hypergeometric series are realized.


Язык: en

Рубрика: Математика/

Тип: Статья

Статус предметного указателя: Неизвестно

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 13

Добавлена в каталог: 13.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2018
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте