Analysis of the chord length distribution of the right circular cone for small chord lengths

The chord length distribution of the right circular cone near the origin is analyzed. The first terms of a series expansion of the correlation function in the origin are given. The third term of this series involves hypergeometric type functions of the shape parameters. The existing logarithmic singularity in the origin is a consequence of the angularity of the edges and the tip of the cone. The expression for the asymptotic scattering intensity I∞(h) is formulated and compared with the exact scattering intensities. I∞ exclusively involves a Porod term and a modified Kirste-Porod term.