Electromagnetic wave radiation from ECCD(electromagnetically coupled coaxial dipole) array antenna is theoretically investigated. Rigorous analytic formulations are derived by an efficient method instead of numerical approximate methods that were used by others. It is assumed that TEM mode is incident on the coaxial cable. The Fourier transform/series technique is used to represent the continuous and discrete modes of scattered fields. The mode-matching is utilized to constitute a set of simultaneous equations for the discrete modal coefficients. Residue calculus is applied to transform the scattered field integral representations into fast convergent series forms, thereby facilitating numerical computations. Numerical computations show the pattern of radiation in terms of the slot numbers and the operating frequency. The analysis procedure in this paper can be useful to design the systems involving the ECCD array antenna.