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

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2018
• Автори: Kenfack Nangho, M., Jordaan, K.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2018
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/209878
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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 {𝔻²ₓPₙ}ₙ₌₂ ∞ , and a generalized Sturm-Liouville type equation. Our treatment of the generalized Bochner theore...