article

q-hypergeometric solutions of q-difference equations

Authors:

Sergei A. Abramov,

Peter Paule,

Marko PetkovšekAuthors Info & Claims

Discrete Mathematics, Volume 180, Issue 1-3

Pages 3 - 22

https://doi.org/10.1016/S0012-365X(97)00106-4

Published: 01 February 1998 Publication History

Abstract

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Schneider C(2023)Refined telescoping algorithms in RΠΣ -extensions to reduce the degrees of the denominators✱Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597073(498-507)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597073
Bostan AYurkevich S(2023)Fast computation of the N-th term of a q-holonomic sequence and applicationsJournal of Symbolic Computation10.1016/j.jsc.2022.07.008115:C(96-123)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.jsc.2022.07.008
Chen SHou QHuang HLabahn GWang R(2022)Constructing minimal telescopers for rational functions in three discrete variablesAdvances in Applied Mathematics10.1016/j.aam.2022.102389141:COnline publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1016/j.aam.2022.102389
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Index Terms

q-hypergeometric solutions of q-difference equations
1. Mathematics of computing
  1. Discrete mathematics
  2. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 February 1998

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Schneider C(2023)Refined telescoping algorithms in RΠΣ -extensions to reduce the degrees of the denominators✱Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597073(498-507)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597073
Bostan AYurkevich S(2023)Fast computation of the N-th term of a q-holonomic sequence and applicationsJournal of Symbolic Computation10.1016/j.jsc.2022.07.008115:C(96-123)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.jsc.2022.07.008
Chen SHou QHuang HLabahn GWang R(2022)Constructing minimal telescopers for rational functions in three discrete variablesAdvances in Applied Mathematics10.1016/j.aam.2022.102389141:COnline publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1016/j.aam.2022.102389
Abramov SBronstein MPetkovšek MSchneider C(2021)On rational and hypergeometric solutions of linear ordinary difference equations in ΠΣ⁎-field extensionsJournal of Symbolic Computation10.1016/j.jsc.2021.01.002107:C(23-66)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1016/j.jsc.2021.01.002
Barkatou MCluzeau TEl Hajj A(2021)On Rational Solutions of Pseudo-linear SystemsComputer Algebra in Scientific Computing10.1007/978-3-030-85165-1_4(42-61)Online publication date: 13-Sep-2021
https://dl.acm.org/doi/10.1007/978-3-030-85165-1_4
Middeke JSchneider C(2019)Towards a direct method for finding hypergeometric solutions of linear first order recurrence systemsACM Communications in Computer Algebra10.1145/3313880.331389152:3(89-91)Online publication date: 16-Feb-2019
https://dl.acm.org/doi/10.1145/3313880.3313891
Ryabenko A(2019)Particular Solutions of Linear Differential and (q-) Difference Systems with Hypergeometric Right-hand SidesProgramming and Computing Software10.1134/S036176881902009945:5(298-302)Online publication date: 1-Sep-2019
https://dl.acm.org/doi/10.1134/S0361768819020099
Abramov SRyabenko AKhmelnov D(2018)Laurent, Rational, and Hypergeometric Solutions of Linear q-Difference Systems of Arbitrary Order with Polynomial CoefficientsProgramming and Computing Software10.1134/S036176881802002044:2(120-130)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1134/S0361768818020020
Middeke JYap CEl Din M(2017)Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant KProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087619(325-332)Online publication date: 23-Jul-2017
https://dl.acm.org/doi/10.1145/3087604.3087619
Foupouagnigni MKoepf WTcheutia DSadjang P(2012)Representations of q-orthogonal polynomialsJournal of Symbolic Computation10.1016/j.jsc.2012.03.00247:11(1347-1371)Online publication date: 1-Nov-2012
https://dl.acm.org/doi/10.1016/j.jsc.2012.03.002
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Recommendations

Linear partial q-difference equations on q-linear lattices and their bivariate q-orthogonal polynomial solutions

Hypergeometric type q-difference equations: Rodrigues type representation for the second kind solution

Difference equations of q-Appell polynomials

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