Representations for Laguerre temperatures

AbstractThe Laguerre difference heat equation ∇nu(n,t)=∂∂u(n,t),where∇nƒ(n)=(n+1)−(2n+a+1)ƒ(n)+(n+a)ƒ(n−1)a⩾0, provides an important discrete analogue of the classical heat equation ∂2u⧸∂x2=∂t. Conditions are established for solutions of this equation to be represented by integral and series transforms