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


Guseinov I. I. , Mamedov B. A.

PHILOSOPHICAL MAGAZINE, vol.87, no.7, pp.1107-1112, 2007 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 87 Issue: 7
  • Publication Date: 2007
  • Doi Number: 10.1080/14786430601023799
  • Journal Name: PHILOSOPHICAL MAGAZINE
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1107-1112

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.