Kant's Observations and Remarks

Coverage is encyclopedic in the first modern treatment of orthogonal polynomials from the viewpoint of special functions. It includes classical topics such as Jacobi Hermite Laguerre Hahn Charlier and Meixner polynomials as well as those (e.g. Askey-Wilson and Al-Salam--Chihara polynomial systems) discovered over the last 50 years and multiple orthogonal polynomials are discussed for the first time in book form. Many modern applications of the subject are dealt with including birth- and death- processes integrable systems combinatorics and physical models. A chapter on open research problems and conjectures is designed to stimulate further research on the subject.