Hypergeometric-type sequences (Q6543086)

The purpose of this paper is to study difference equations of the form \N\[\NP(n)a_{n+m}=Q(n)a_ n,\N\]\Nwhere \(P\) and \(Q\) are polynomials. The solutions for \(m>1\) are called \(m\)-fold hypergeometric. The main theorem states that the solutions form a subring of the ring of holonomic sequences. In several examples, sequences defined by trigonometric functions with linear arguments in the index and \(\pi\) are studied with the help of computer programs.