We develop algorithms for computations of Green’s function and its Fourier coefficients, $F_n(z;s)$, on Fuchsian groups with one cusp. An analogue of a Rankin-Selberg bound for $F_n(z;s)$ is presented.
"Computations of Green's Function and Its Fourier Coefficients on Fuchsian Groups." Experiment. Math. 19 (3) 317 - 334, 2010.