Lectures on Orthogonal Polynomials and Special Functions

doi:10.1017/9781108908993

Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-ix
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List of Contributors
pp x-x
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Preface
pp xi-xvi
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1 - Exceptional Orthogonal Polynomials via Krall Discrete Polynomials
pp 1-75
- By Antonio J. Durán
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2 - A Brief Review of q-Series
pp 76-130
- By Mourad E.H. Ismail
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3 - Applications of Spectral Theory to Special Functions
pp 131-212
- By Erik Koelink
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4 - Elliptic Hypergeometric Functions
pp 213-279
- By Hjalmar Rosengren
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5 - Combinatorics of Orthogonal Polynomials and their Moments
pp 280-334
- By Jiang Zeng
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Lectures on Orthogonal Polynomials and Special Functions

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Contents

Frontmatter
pp i-iv

Contents
pp v-ix

List of Contributors
pp x-x

Preface
pp xi-xvi

1 - Exceptional Orthogonal Polynomials via Krall Discrete Polynomials
pp 1-75

2 - A Brief Review of q-Series
pp 76-130

3 - Applications of Spectral Theory to Special Functions
pp 131-212

4 - Elliptic Hypergeometric Functions
pp 213-279

5 - Combinatorics of Orthogonal Polynomials and their Moments
pp 280-334

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Lectures on Orthogonal Polynomials and Special Functions

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