Difference equations related to Jacobi-type pencils
Sergey M. Zagorodnyuk · The Journal of Difference Equations and Applications · 2018
In this paper we study various difference equations related to Jacobi-type pencils. By a Jacobi-type pencil one means the following pencil: J5−λJ3, where J3 is a Jacobi matrix and J5 is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the second subdiagonal. The basic set of solutions for the corresponding 4th order difference equation is constructed. Spectral properties of the truncated pencil and some special matrix orthogonality relations are investigated. Classical type orthogonal polynomials satisfying a 4th order differential equation are constructed.