Regular boundary problems for a five-term recurrence relation

Claude Elias Billigheimer

Vol. 35 (1970), No. 1, 23–51

DOI: 10.2140/pjm.1970.35.23

Abstract

We consider in this paper boundary problems for the fiveterm scalar recurrence relation

(1.1)

where the coefficients a_n,b_n,c_n,d_n are real, a_n,d_n > 0 and λ is a complex parameter, with boundary conditions of the typical form

(1.2)

and

(1.3)

for some integer m ≧ 0, and real numbers h,k.

We derive oscillation properties, orthogonality relations and associated eigenvector expansion theorems for solutions of (1.1), (1.2), (1.3), and then discuss the solution of boundary problems for the corresponding inhomogeneous recurrence relation in terms of a Green’s function.

Mathematical Subject Classification

Primary: 39.20

Secondary: 34.00

Milestones

Received: 17 September 1968

Revised: 1 April 1970

Published: 1 October 1970