JournalszaaVol. 26 , No. 4DOI 10.4171/zaa/1338

Linear <em>q</em>-Difference Equations

  • M.H. Abu Risha

    Cairo University, Egypt
  • M.H. Annaby

    Cairo University, Egypt
  • Z.S. Mansour

    Cairo University, Egypt
  • Mourad E. H. Ismail

    University of Central Florida, Orlando, United States
Linear <em>q</em>-Difference Equations cover

Abstract

We prove that a linear q-difference equation of order n has a fundamental set of n-linearly independent solutions. A q-type Wronskian is derived for the n-th order case extending the results of Swarttouw--Meijer (1994) in the regular case. Fundamental systems of solutions are constructed for the n-th order linear q-difference equation with constant coefficients. A basic analog of the method of variation of parameters is established.