Ebook: Classical Orthogonal Polynomials of a Discrete Variable

While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.

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While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Classical Orthogonal Polynomials....Pages 2-17
Classical Orthogonal Polynomials of a Discrete Variable....Pages 18-54
Classical Orthogonal Polynomials of a Discrete Variable on Nonuniform Lattices....Pages 55-168
Front Matter....Pages 169-169
Classical Orthogonal Polynomials of a Discrete Variable in Applied Mathematics....Pages 170-220
Classical Orthogonal Polynomials of a Discrete Variable and the Representations of the Rotation Group....Pages 221-283
Hyperspherical Harmonics....Pages 284-359
Back Matter....Pages 361-374

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While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Classical Orthogonal Polynomials....Pages 2-17
Classical Orthogonal Polynomials of a Discrete Variable....Pages 18-54
Classical Orthogonal Polynomials of a Discrete Variable on Nonuniform Lattices....Pages 55-168
Front Matter....Pages 169-169
Classical Orthogonal Polynomials of a Discrete Variable in Applied Mathematics....Pages 170-220
Classical Orthogonal Polynomials of a Discrete Variable and the Representations of the Rotation Group....Pages 221-283
Hyperspherical Harmonics....Pages 284-359
Back Matter....Pages 361-374
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