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This book defines sets of orthogonal polynomials and derives a
number of properties satisfied by any such set. It continues by
describing the classical orthogonal polynomials and the additional
properties they have.The first chapter defines the orthogonality
condition for two functions. It then gives an iterative process to
produce a set of polynomials which are orthogonal to one another
and then describes a number of properties satisfied by any set of
orthogonal polynomials. The classical orthogonal polynomials arise
when the weight function in the orthogonality condition has a
particular form. These polynomials have a further set of properties
and in particular satisfy a second order differential equation.Each
subsequent chapter investigates the properties of a particular
polynomial set starting from its differential equation.
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