Uniformly charged bodies with various symmetries are of great interest to many models in several disciplines. In particular, there are numerous physical and biological systems that contain rod-like charged particles. In this work, we consider a system of two identical uniformly charged rods and calculate their electrostatic interaction energy for a special case of orientation between them. A first approach that relies on standard integration methods allows us to obtain an exact analytic expression for such an interaction in this case. Application of a second different method to the same problem leads to mathematical expressions involving generalized hypergeometric functions, a class of special functions not frequently encountered in the field. Comparison of the two results leads to interesting mathematical identities that might be of interest to a broad audience of researchers working in mathematical and physical sciences.