A unified treatment of the lattice Green function, generalized Watson integral and associated logarithmic integral for thed-dimensional hypercubic lattice

Using multinomial expansion theorems, a unified approximation for the lattice Green function, generalized Watson integral and associated logarithmic integral for the d-dimensional hypercubic lattice is presented. The validity of this approximation is tested by other calculation methods. The approximate formulas derived are satisfactory to all other approximations and are a most suitable solution for the study of related physical properties of solids. Some examples of the effectiveness of this methodology are presented.