These are OP’s on the interval with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at −1 and 1 to the weight function for the Jacobi polynomials. For further information see Koornwinder (1984b) and Kwon et al. (2006).
Similar OP’s can also be constructed for the Laguerre polynomials; see Koornwinder (1984b, (4.8)).
These are polynomials in one variable that are orthogonal with respect to a number of different measures. They are related to Hermite-Padé approximation and can be used for proofs of irrationality or transcendence of interesting numbers. For further information see Ismail (2005, Chapter 23).
These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. Classes of such polynomials have been found that generalize the classical OP’s in the sense that they satisfy second-order matrix differential equations with coefficients independent of the degree. For further information see Durán and Grünbaum (2005).