Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part

Orthogonality of the Jacobi and Laguerre polynomials, Pn(α,β) and Ln(α), is established for α,β∈C∖Z−,α+β≠−2,−3,… using the Hadamard finite part of the integral which gives their orthogonality in the classical cases. Riemann–Hilbert problems that these polynomials satisfy are found.The results are formally similar to the ones in the classical case (when ℜα,ℜβ>−1ℜα,ℜβ>−1).