Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F2

  • Zine el abidine Bentalha


Exact analytical representation for the Coulomb matrix elements by means of Appell’s double series F2 is derived. The finite sum obtained for the Appell function F2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.


Quantum Hall fluid Electron gas Hypergeometric functions Appell functions 

Mathematics Subject Classification (2010)

33Cxx 33C65 



I would like to thank the anonymous reviewers for the valuable suggestions given for improving presentation of the paper. Particularly, I would like to thank greatly the anonymous reviewer who evoked questions that allowed to make clear the deep insights of this paper and its impact on future works within this line of research.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Theoretical Physics LaboratoryUniversity of TlemcenTlemcenAlgeria

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