Linear $q$-Difference Equations

M.H. Abu Risha; M.H. Annaby; Mourad E. H. Ismail; Z.S. Mansour

doi:10.4171/zaa/1338

JournalszaaVol. 26, No. 4pp. 481–494

Linear $q$ -Difference Equations

M.H. Abu Risha
Cairo University, Egypt
M.H. Annaby
Cairo University, Egypt
Mourad E. H. Ismail
University of Central Florida, Orlando, United States
Z.S. Mansour
Cairo University, Egypt

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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.

Cite this article

M.H. Abu Risha, M.H. Annaby, Mourad E. H. Ismail, Z.S. Mansour, Linear $q$ -Difference Equations. Z. Anal. Anwend. 26 (2007), no. 4, pp. 481–494

DOI 10.4171/ZAA/1338