Analytic continuation of the Lauricella function with arbitrary number of variables

The Lauricella function F(N) D, which is a generalized hypergeometric function of N variables, and a corresponding system of partial differential equations are considered. For an arbitrary N, we give a complete collection of analytic continuation formulas of F(N) D. This formulas give representation of the Lauricella function outside the polydisk in the form of a linear combination of other generalized hypergeometric series that are solutions of the same system of partial differential equations, which is also satisfied by the function F(N) D. The obtained hypergeometric series are N-dimensional analogues of the Kummer solutions well known in the theory of the classical hypergeometric Gauss equation. The obtained analytic continuation formulas provide an effective algorithm for computation of the Lauricella function F(N) D. © 2017 Informa UK Limited, trading as Taylor & Francis Group.

Авторы
Bezrodnykh S.I. 1, 2, 3
Издательство
Taylor and Francis Ltd.
Номер выпуска
1
Язык
Английский
Страницы
21-42
Статус
Опубликовано
Том
29
Год
2018
Организации
  • 1 Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russian Federation
  • 2 Sternberg Astronomical Institute, Lomonosov Moscow State University, Moscow, Russian Federation
  • 3 Peoples Friendship University of Russia (RUDN University), Moscow, Russian Federation
Ключевые слова
analytic continuation formulas; Barnes-type integrals; Lauricella function; Multiple hypergeometric functions; Schwartz–Christoffel integral; systems of PDEs
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6928/
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