| Abstract: | Approximations using the generalized Laguerre polynomials are investigated in thispaper.Error estimates for various orthogonal projections are established.These estimatesgeneralize and improve previously published results on the Laguerre approximations.Asan example of applications,a mixed Laguerre-Fourier spectral method for the Helmholtzequation in an exterior domain is analyzed and implemented.The proposed method enjoysoptimal error estimates,and with suitable basis functions,leads to a sparse and symmetriclinear system. |
