Lagrange expansion in terms of Fadle-Papkovich functions in the boundary-value problem for a semistrip

A strip with constant stresses on the cut: Exact solutions

“…To determine this constant, let us introduce (as, for example, in Refs. [16,18]) a biorthogonal function with zero index as follows:…”

“…To determine this constant, let us introduce (as, for example, in Refs. [16, 18]) a biorthogonal function with zero index as follows: $$\begin{equation}\int\limits_{{ - \infty }}^{\infty }{{\xi (\lambda ,y){U}_0(y)dy}} = - \frac{\nu }{2}L(\lambda ).\end{equation}$$…”