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( p , q )‐Sturm‐Liouville problems and their orthogonal solutions
Author(s) -
Soleyman F.,
Sadjang P. Njionou,
MasjedJamei M.,
Area I.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4800
Subject(s) - mathematics , sturm–liouville theory , hypergeometric function , hypergeometric distribution , norm (philosophy) , limiting , polynomial , orthogonal polynomials , square (algebra) , pure mathematics , mathematical analysis , boundary value problem , mechanical engineering , geometry , political science , law , engineering
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.