Agnes Scott College

Sister Mary Celine Fasenmyer

A Note On Pure Recurrence Relations
The American Mathematical Monthly, Vol. 56, No. 1 (Jan. 1949), 14-17


The pure recurrence relations of many of the classical polynomials, for example, the Laguerre, and in particular those of the hyper-geometric type, such as the Jacobi, Legendre, and so on, are readily obtained by the method exhibited in this paper. Many of the recently studied polynomials, as Rice's Hn(ξ, ρ, ν), Bateman's Jnu,v, and Bateman's Zn(t), lend themselves to this treatment. It is particularly useful for polynomials which do not form an orthogonal set, and for which there are not available the extremely simple methods of the theory of orthogonal polynomials.