On the convergence of orthogonal eigenfunction series

✍ Scribed by John G. Fikioris

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 640 KB
• Volume: 27
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/0378-4754(85)90072-2

✦ Synopsis

The method of Watson's Transformation, well known in high frequency scattering, is applied to a two-dimensional, orthogonal eigenfunction series of rectangular harmonic functions, which provides the solution to a typical boundary value problem of Laplace's equation. A new infinite, so-called residue, series is obtained exhibiting convergence properties stronger than, in certain respects,and complementary to the original eigenfunction series. Convergence of the two series and of their derivatives is further compared and tested near points of discontinuity. "Extraction" of the discontinuous term out of the original series and reexpansion of the solution providesa thirdeigenfunction series with uniform convergence in the whole region and good convergence near the singularities of the solution. Eigenfunction series of other boundary value problems are,also, discussed and similarities with the evaluation of complicated Fourier or Sommerfeld integrals via contour integration are pointed out. 1.