The evaluation of complex radiation impedance for a square piston source on an infinite circularcylindrical baffle is associated to the Greenspon-Sherman formulation for which novel evaluation methods are proposed. Unlike existing methods results are produced in a very wide range of frequencies and source semi-angles with controllable precision. For this reason closed-form expressions are used to describe the truncation errors of all integrals and infinite sums involved. Impedance values of increased accuracy are also provided in tabulated form for engineering use and a new radiation mass-load model is derived for low-frequencies.