Semi-infinite body, 1-D, Steady-Periodic GF

X10 Semi-infinite body, $0<x<\infty$, with $G=0$ (Dirichlet) at x=0.

$$G_{X10}(x,x^{\prime},\omega)=\frac{1}{2 \alpha \sigma} [e^{- \sigma \vert x-x'\vert}-e^{- \sigma \vert x+x'\vert}]$$

$$\sigma=(1+\it {i})\sqrt{\frac{\omega}{2\alpha}}$$

X20 Semi-infinite body, $0<x<\infty$, with $\partial{G}/\partial{x}=0$ (Neumann) at x=0.

$$G_{X20}(x,x^{\prime},\omega)=\frac{1}{2 \alpha \sigma} [e^{- \sigma \vert x-x'\vert}+e^{- \sigma \vert x+x'\vert}]$$

X30 Semi-infinite body, $0<x<\infty$, with $-\it {k}\partial{G}/\partial{x}+\it {h}G=0$ (Convection) at x=0.

$$G_{X30}(x,x^{\prime},\omega)=\frac{1}{2 \alpha \sigma} [e^{- \sigma \vert x-x'\vert}+R \cdot e^{- \sigma \vert x+x'\vert}]$$

$$R~=~ \frac{k \sigma - h}{k \sigma + h}$$