R factors in X-ray fiber diffraction. I. Largest likely R factors for N overlapping terms

Simple expressions are obtained for the largest likely R factor in X-ray fiber diffraction recently derived by Stubbs [Acta Cryst. (1989), A45, 254-258]. These generalize the largest likely R factors obtained by Wilson [Acta Cryst. (1950), 3, 397-399] for centric and acentric crystals. Expressions are obtained in terms of special functions and as finite series that simplify the calculation of R factors. These may be useful for further analysis and understanding of the effects of particle diameter and symmetry and diffraction data resolution on the reliability of structure determinations.