The F_N method, originated by C. E. Siewert, is developed for a bare, axially infinite critical cylinder. The full-range completeness and orthogonality properties of the singular eigenfunctions are used to derive an expression for the emerging angular flux, which is represented by a power series. The resulting equations are reduced to matrix form and computer solved.

Examples of the results of this method for different parameters are presented. Comparisons with other models are made. A fourth order approximation was found to be sufficient to achieve up to four digit agreement with benchmark values.