Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Series equations involving Jacobi polynomials and mixed boundary-value problems of the Laplace equation

Authors: Masaaki Shimasaki and Takeshi Kiyono
Journal: Quart. Appl. Math. 31 (1973), 53-73
MSC: Primary 45F10
DOI: https://doi.org/10.1090/qam/417713
MathSciNet review: 417713
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Abstract: A formal analysis of series equations involving Jacobi polynomials is given. $ \left( {2N + 1} \right)$ series equations involving Jacobi polynomials are reduced to a set of $ N$ simultaneous Fredholm integral equations which can be solved numerically by the use of the Legendre-Gauss quadrature formula. In case of triple series equations the result is in agreement with that of Lowndes. Besides triple series equations, certain quadruple series equations can be also reduced to a single Fredholm integral equation of the second kind. Owing to the introduction of an arbitrary weight factor, the theory is feasible for the analysis of various many-part mixed boundary-value problems of the Laplace equation. As an example, special cases of certain trigonometric series equations are discussed in detail in connection with an electrostatic problem.

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DOI: https://doi.org/10.1090/qam/417713
Article copyright: © Copyright 1973 American Mathematical Society

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