## q-Series and partitionsThis volume contains the proceedings of the workshop held for the Applied Combinatorics program in March, 1988. The central idea of the workshop is the recent interplay of the classical analysis of q-series, and the combinatorial analysis of partitions of intergers. Many related topics are discussed, including orthogonal polynomials, the Macdonald conjectures for root systems, and related integrals. Those people interested in combinatorial enumeration and special functions will find this volume of interest. Recent applications of q-series (and related functions) to exactly solvable statistical mechanics models and to statistics makes this volume of interest to non-specialists. Included are several expository papers, and a series of papers on new work on the unimodality of the q-binomial coefficient. |

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### Contents

On the Proofs of the RogersRamanujan Identities l | 1 |

Bibasic Summation Transformation and Expansion Formulas | 15 |

Identities | 35 |

Copyright | |

10 other sections not shown

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### Common terms and phrases

affine root systems algebra Amer Anal analogs Applications aq/b Askey Bailey basic hypergeometric series block Bressoud classical Clausen's formula coefficients constant term Coxeter group define Dennis Stanton denote derive Doron Zeilberger Dyson eigenvalues element equations evaluate expansion finite follows g-analogue G.E. Andrews Gasper Gaussian polynomials given hypergeometric functions implies inequalities inner product invariant irreducible Ismail Jacobi polynomials Laguerre polynomials Lemma linear Mac-Meh Macdonald identities Math matrix monomially monomially bounded nomials nonnegative O'Hara's obtain ordinary rook polynomials orthogonal polynomials orthogonal with respect parameter partitions permutations positive problem Proc proof prove q-Series quadratic Rahman Ramanujan recurrence relations relative height result Rogers-Ramanujan identities rook functor satisfying Schur Selberg's integral sequence set of conditions SIAM side solution subset summation formula symmetric and unimodal Theorem theory transformation formula unimodality weight function Weyl group Zeilberger zeros of orthogonal zonal polynomials