## Special Functions 2000: Current Perspective and Future Directions: current perspective and future directions : [proceedings of the NATO Advanced Study Institute on Special Functions 2000: Current Perspective and Future Directions, Tempe, Arizona, USA, 29 May-9 June 2000]Joaquin Bustoz, Mourad Ismail, Sergeĭ Konstantinovich Suslov The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painleve classification. |

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### Contents

Baileys transform lemma chains and tree | 1 |

RiemannHilbert problems for multiple orthogonal polynomials | 23 |

Flowers which cannot yet see growing in Ramanujans garden of hypergeometric series elliptic functions and qs | 61 |

Orthogonal rational functions and continued fractions | 87 |

Orthogonal polynomials and reflection groups | 111 |

an overview | 129 |

some new perspectives | 141 |

Lectures on qorthogonal polynomials | 179 |

Special functions defined by analytic difference equations | 281 |

The factorization method selfsimilar potentials and quantum algebras | 335 |

Generalized eigenvalue problem and a new family or rational functions biorthogonal on elliptic grids | 365 |

Orthogonal Polynomials and Combinatorics | 389 |

Basic exponential functions on a qquadratic grid | 411 |

Projection operator method for quantum groups | 457 |

Uniform asymptotic expansions | 489 |

Exponential asymptotics | 505 |

### Other editions - View all

Special Functions 2000: Current Perspective and Future Directions Joaquin Bustoz,Mourad E. H. Ismail,Sergei Suslov No preview available - 2014 |

Special Functions 2000: Current Perspective and Future Directions Joaquin Bustoz,Mourad E.H. Ismail,Sergei Suslov No preview available - 2001 |

### Common terms and phrases

Amer analogue analytic Askey Askey-Wilson function Askey-Wilson polynomials associated asymptotic basic hypergeometric basic hypergeometric series Berndt big g-Jacobi biorthogonal Bustoz classical orthogonal polynomials coefficients Comput condition continued fraction convergence corresponding Darboux transformations defined denote difference equations discrete eigenfunctions eigenvalue elliptic expansion explicit exponential F. A. Griinbaum factorization finite formula function transform g-analogues g-Bessel function gamma function given hypergeometric function hypergeometric series identities infinite integral Jacobi function Jacobi polynomials limit transition linear M. E. H. Ismail Math Mathematics matrix method minimal solution modular multiple orthogonal polynomials notebook obtain orthogonal polynomials orthogonality relation parameters partition function Phys Pn(z poles proof properties quantum groups Ramanujan rational functions recurrence relation representation Riemann-Hilbert problem Rn(z Rogers-Ramanujan root satisfy second order Section sequence special functions spectral Suslov Theorem theory three-term tions trigonometric variable vector weight function Wilson polynomials zeros zeta function