An integral of the type integral q(1)\(2)+mu(1)(2))(m+1)(\q-q(2)\(2)+m
u(2)(2))(n+1) is expressed by contour integration as a sum of two fini
te series for any finite values of l, m, n, thus avoiding parametric d
ifferentiation of a complicated closed form expression with respect to
mu(0), mu(1), mu(2). This integral is frequently encountered in studi
es of atomic, molecular, nuclear and plasma physics.