TITLE:
Matrix Boundary Value Problem on Hyperbola
AUTHORS:
Shaohua Fan
KEYWORDS:
Hyperbola, Matrix Boundary Value Problem, Orthogonal Polynomial
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.4,
April
18,
2023
ABSTRACT: We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only one. Secondly, a special boundary value problem of lower triangular matrix is presented and transformed into four related boundary value problems. Finally, Liouville theorem and Painlevé theorem and pseudo-orthogonal polynomials are used to give solutions.