# Evaluation of a general three-denominator Lewis integral

## Description

Abstract An integral of the type. ∫ dq (q^2 +μ^2 _0 )^(l+1)(|q-q_1 |^2 +μ^2 _1 )^(m+1)(|q-q_2 |^2 +μ^2 _2 )^(n+1). is expressed by contour integration as a sum of two finite series for any finite values of l, m, n, thus avoiding parametric differentiation of a complicated closed form expression with respect to μ_0 , μ_1 , μ_2 . This integral is frequently encountered in studies of atomic, molecular, nuclear and plasma physics. Title of program: LEWIS Catalogue Id: ADCO_v1_0 Nature of problem Structural and collisional studies in atomic, molecular and nuclear physics often encounter a certain type of 3-denominator integrals in the course of the calculations [1]. These integrals (called here general Lewis integrals [2]) appear naturally whenever two or more centres of force are present and relative coordinates of the interacting particles are involved. We derive a closed analytic form for these integrals and demonstrate by a few examples the usefulness of the results. Versions of this program held in the CPC repository in Mendeley Data ADCO_v1_0; LEWIS; 10.1016/0010-4655(95)00121-4 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)