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Abstract
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.
Acknowledgement
The authors wish to thank an anonymous reviewer for their helpful suggestions which have greatly improved the presentation of this paper.