Sturm-Liouville Problem in Quantum Calculus

2006/08/04 by Ahmed Fitouhi, Fitouhi, Ahmed, Akram Nemri +3
Mathematics · Physics and Astronomy · #26D15 #33D05 #33D15 #33D60 #33D90 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:26D15 #msc:33D05 #msc:33D15 #msc:33D60 #msc:33D90

paper · pdf · doi:10.48550/arxiv.math-ph/0608015

16 pages

arxiv created 2006/08/04 · arxiv updated 2009/12/01

Abstract

This paper aims to study the q-analogue of the Sturm Liouville problem and to give an asymptotic behaviour at infinity for its solution '. Additionally, we establish an asymptotic expansion of the q-Bessel function j_α for α>-1/2. We are not in situation to claim that our results are new but they have the advantage to show that the method used by Agranovich and Marchenko remain true.

Related

• The Modified q-Bessel Functions and the q-Bessel-Macdonald Functions
• q-Sturm-Liouville theory and the corresponding eigenfunction expansions
• The asymptotic behavior of q-exponentials and q-Bessel functions
• q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations
• A β-Sturm Liouville problem associated with the general quantum operator