Orthogonality of Jacobi polynomials with general parameters Kuijlaars, A. B. J. Martínez-Finkelshtein, A. Orive, R. Jacobi polynomials Orthogonality Rodrigues formula Zeros In this paper we study the orthogonality conditions satisfied by Jacobi polynomials Pn(α,β) when the parameters α and β are not necessarily >−1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of contours in the plane. In all cases we show that the orthogonality conditions characterize the Jacobi polynomial Pn(α,β) of degree n up to a constant factor. 2014-07-10T07:12:55Z 2014-07-10T07:12:55Z 2005 journal article Kuijlaars, A.B.J.; Martínez-Finkelshtein, A.; Orive, M. Orthogonality of Jacobi polynomials with general parameters. Electronic Transactions on Numerical Analysis (ETNA), 19: 1-17 (2005). [http://hdl.handle.net/10481/32635] 1068-9613 http://hdl.handle.net/10481/32635 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Kent State University. Institute of Computational Mathematics