Evaluate More General Integrals Involving Universal Associated Legendre Polynomials via Taylor's Theorem

A few important integrals involving the product of two universal associated Legendre polynomials , and x^2a(1 - x²)^-p-1, x^b(1 ± x)^-p-1 and x^c(1 -x²)^-p-1 (1 ± x) are evaluated using the operator form of Taylor's theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e. l′ ≠ k^′ and m′ ≠ n′ Their selection rules are also given. We also verify the correctness of those integral formulas numerically.