Summing \(P_ n(\cos \,\theta)/p(n)\) for certain polyonomials p(n) (Q802813)

Procedures are given to sum infinite Legendre series with terms of the form \(P_ n(\cos \theta)/p(n)\), where p(n) is a polynomial in \((2n+1)^ 2\), with roots that are perfect squares, and p(n)\(\neq 0\) for all \(n\geq N\), the lower limit of the infinite series. These series are needed in problems of computational chemistry, and may be of use in other applications of potential theory. An analytical approach is needed, since the series converge too slowly for direct numerical summation.