Influence functions appropriate for the boundary-element method for the Lap
lace equation are given for the infinite and semi-infinite strip. The metho
d of Green's functions is used to produce single-sum series for the influen
ce functions, which reflect the domain shape and the boundary conditions. B
oundary conditions of type 1, 2, and 3 are treated. Series convergence is i
mproved by identifying slowly converging terms and replacing them with full
y summed polynomial forms. Numerical examples are given.