A new formula for Coulomb matrix elements in the lowest Landau level in disk geometry

Abstract As previously shown, the elements of the Coulomb matrix (CMEs), in the lowest Landau level (LLL) and in the disk geometry, can be expressed by means of Appell F 2 double hypergeometric function, only the corresponding series is a double sum of terms with alternating signs. In this work, for reasons of optimizing the computational efficiency of CMEs, we transform these sums into sums of positive terms using the properties of Appell F 2 double hypergeometric function. Thus, a new formula for CMEs is derived. Also, a comparison is conducted between the times elapsed when evaluating CMEs by the well-known formula of Tsiper or the new derived formula.