We consider a vertical circular cylinder on which the vertical variation of water diffraction waves is to be represented by a series of Laguerre functions  using Laguerre Polynomials . The variation is assumed to be of the form  with the integer n depending on the radius of cylinder. Generally, the integer n increases for a cylinder of larger diameter. The usual approximation by Laguerre functions is extended by introducing a scale parameter. The convergence of Laguerre series is then dependent on the value of the scale parameter s. The analytical and numerical computations of series coefficients are performed to study the number of series terms to keep the same accuracy. Indeed, the choice of integer n depends on the scale parameter. Furthermore, diffraction waves generated by a semi-sphere inside the cylinder are evaluated on the cylinder surface. It is shown that the approximation by Laguerre series for diffraction waves on the cylinder is effective. This work provides important information for the choice of the radius of control surface in the domain decomposition method for solving hydrodynamic problems of body-wave interaction.