Structure Relations of Classical Orthogonal Polynomials in the Quadratic and q-Quadratic Variable

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Kenfack Nangho, M., Jordaan, K.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209878
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Structure Relations of Classical Orthogonal Polynomials in the Quadratic and q-Quadratic Variable / M. Kenfack Nangho, K. Jordaan // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 28 назв. — англ.

We prove an equivalence between the existence of the first structure relation satisfied by a sequence of monic orthogonal polynomials {Pₙ}ₙ₌₀ ∞, the orthogonality of the second derivatives { ²ₓPₙ}ₙ₌₂ ∞ , and a generalized Sturm-Liouville type equation. Our treatment of the generalized Bochner theore...