Properties of eigenfunction expansion form for the rigid line problem in dissimilar media

this paper, the eigenfunction expansion form (abbreviated as EEF) in the rigid line problem in dissi.milar media is derived. The properties of the EEF are discussed in detail. After using Betti’s rec:iprocal theorem for a particular contour, several path independent integrals are obtained. All the coefficients in the EEF, including the & and I& values can be related to the corresponding path independent integrals. It is found that the J-integral takes a definitely negative value in the preseent case. A possibility for formulating the weight function is also suggested. Finally, a boundary value problem for a single rigid line embedded in dissimilar media is studied and solved