(p, q)‐Sturm‐Liouville problems and their orthogonal solutions. (12th February 2018)

• Record Type: Journal Article
• Authors: Soleyman, F.; Sadjang, P. Njionou; Masjed‐Jamei, M.; Area, I.
• Other Names: Anguelov Roumen guestEditor.; Banasiak Jacek guestEditor.; Debbouche Amar guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 18(2018)
• Page Start: 8997
• Page End: 9009
• Publication Date: 2018-02-12
• Subjects: (p, q)‐Sturm‐Liouville problems -- (p, q)‐Pearson difference equation -- (p, q)‐orthogonal solutions -- (p, q)‐integral -- (p, q)‐difference operator; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4800
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we introduce ( p, q )‐Sturm‐Liouville problems and prove that their solutions are orthogonal with respect to a ( p, q )‐integral space. We then present some illustrative examples for this kind of problems and obtain the ( p, q )‐hypergeometric representation of the polynomial solutions together with their 3‐term recurrence relations. We also compute the norm square value of the polynomial solutions and obtain their limiting cases in the sequel.