Analytical Solution of the Three-Dimensional Laplace Equation in Terms of Linear Combinations of Hypergeometric Functions

被引：8

作者：

Lupica, Antonella ^{[1
]}

Cesarano, Clemente ^{[2
]}

Crisanti, Flavio ^{[1
]}

Ishkhanyan, Artur ^{[3
,4
]}

机构：

[1] Univ Tuscia, Dept Econ Engn Soc & Business Org DEIm, I-01100 Viterbo, Italy

[2] Int Telemat Univ Uninettuno, Sect Math, I-00186 Rome, Italy

[3] Russian Armenian Univ, Dept Gen Phys, Yerevan 0051, Armenia

[4] Inst Phys Res, Ashtarak 0203, Armenia

来源：

MATHEMATICS | 2021年 / 9卷 / 24期

关键词：

Laplace equation; Heun equation; analytic solution; cap-cyclide geometry; standard toroidal geometry; hypergeometric functions; MHD-EQUILIBRIA;

D O I：

10.3390/math9243316

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present some solutions of the three-dimensional Laplace equation in terms of linear combinations of generalized hyperogeometric functions in prolate elliptic geometry, which simulates the current tokamak shapes. Such solutions are valid for particular parameter values. The derived solutions are compared with the solutions obtained in the standard toroidal geometry.

引用

页数：16

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