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3 results

  • On classical irregular q-difference equations

  • Part of
  • Julien Roques
  • Journal:
    Compositio Mathematica / Volume 148 / Issue 5 / September 2012
    Published online by Cambridge University Press:
    25 July 2012, pp. 1624-1644
    Print publication:
    September 2012
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  • The primary aim of this paper is to (provide tools to) compute Galois groups of classical irregular q-difference equations. We are particularly interested in quantizations of certain differential equations that arise frequently in the mathematical and physical literature, namely confluent generalized q-hypergeometric equations and q-Kloosterman equations.

  • q-Integral and Moment Representations for q-Orthogonal Polynomials

  • Mourad E. H. Ismail, Dennis Stanton
  • Journal:
    Canadian Journal of Mathematics / Volume 54 / Issue 4 / 01 August 2002
    Published online by Cambridge University Press:
    20 November 2018, pp. 709-735
    Print publication:
    01 August 2002
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  • We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for $q$-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the $q$-exponential function $\text{ }{{\varepsilon }_{q}}$.