International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 16, Pages 807-825

Eigenstructure of the equilateral triangle. Part III. The Robin problem

Brian J. McCartin

Department of Applied Mathematics, Kettering University, 1700 West Third Avenue, Flint 48504-4898, MI, USA

Received 16 June 2003

Copyright © 2004 Brian J. McCartin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Lamé's formulas for the eigenvalues and eigenfunctions of the Laplacian on an equilateral triangle under Dirichlet and Neumann boundary conditions are herein extended to the Robin boundary condition. They are shown to form a complete orthonormal system. Various properties of the spectrum and modal functions are explored.