Projects and Assignments in Pure Mathematics

Orthogonal and q-orthogonal polynomials

Dealing with vectors is easy if we have a nice basis to represent them. Many spaces of functions can be naturally viewed as vector space thus raising a question about suitable bases. Such bases are oftenly provided by families of orthogonal polynomials which have many remarkable properties themselves.

Books

G. Szego, Orthogonal polynomials, AMS, 1959.
B. Simon, OPUC on one foot, Bull. Amer. Math. Soc. 42 (2005), 431-460. http://www.ams.org/journals/bull/2005-42-04/

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