The overlap integral of three associated Legendre polynomials Original Research Article

A closed formula with a double sum is obtained for the overlap integral of three associated Legendre polynomials (ALPs). The result is applicable to integral involving the ALP with arbitrary degree l and order m. Special overlap integrals, including the cases m3 = m1 + m2 or |m1 – m2|, are presented. A general formula for the overlap integral of an arbitrary number of ALPs is also developed.