Hypergeometric Functions II (q-analogues)

2013/09/20 by I. G. Macdonald, Macdonald, Ian G. · 3 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1309.5208

openalex publication_date 2013/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the typewritten version of a handwritten manuscript which was completed by Ian G. Macdonald in 1987 or 1988. It is the sequel to the manuscript "Hypergeometric functions I." The two manuscripts are very informal working papers, never intended for formal publication. Nevertheless, copies of the manuscripts have circulated widely, giving rise to quite a few citations in the subsequent 25 years. Therefore it seems justified to make the manuscripts available for the whole mathematical community. The author kindly gave his permission that typewritten versions be posted on arXiv.

Cited by

• Superintegrability for some (q,t)-deformed matrix models
• A Characterization of Macdonald's Jack Hypergeometric Series _pF_q(x;α) and _pF_q(x,y;α) via Differential Equations
• A Nekrasov–Okounkov formula for Macdonald polynomials

Related

• Hypergeometric Functions I
• Lecture notes for an introductory minicourse on q-series
• Additions to the formula lists in "Hypergeometric orthogonal polynomials and their q-analogues" by Koekoek, Lesky and Swarttouw
• Holonomic Tools for Basic Hypergeometric Functions
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