Differential and Difference Equations pp 113-123 | Cite as

# Dictionary of Difference Equations with Polynomial Coefficients

## Abstract

In this chapter we list the difference equations for some of the classical functions and polynomials of mathematical physics. These difference equations have coefficients which are polynomials in the argument of the difference equation, their degree ranging from zero (i.e., constant coefficients) for the Tchebichef polynomials \(T_{n}(x)\) and \(U_{n}(x)\) to three for the Jacobi polynomials \(P_{n}^{(\alpha , \beta )}(x)\) and \(Q_{n}^{(\alpha , \beta )}(x)\). We list only those difference equations in which only one parameter varies (note, for example, Eq. (8.16), in which only \(\nu \) varies, or Eq. (8.17), in which only \(\mu \) varies).