Description

Book Synopsis
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.

Classical Orthogonal Polynomials, The

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A Hardback by Brian George Spencer Doman

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    View other formats and editions of Classical Orthogonal Polynomials, The by Brian George Spencer Doman

    Publisher: World Scientific Publishing Co Pte Ltd
    Publication Date: 12/11/2015
    ISBN13: 9789814704038, 978-9814704038
    ISBN10: 9814704032
    Also in:
    Numerical analysis

    Description

    Book Synopsis
    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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