On the solutions of the Airy equation and their zeros

We present some observations on the solutions of Airy equation and the distribution of their zeros. Through the introduction of two parameters, we characterize the general solutions of the Airy equation by looking at a particular solution of an equivalent parametric equation. Addition formulae, generalizing those of the trigonometric functions, are obtained. A recursion for the zeros is given and a characterization of the distribution of the zeros by varying the values of the parameters is described. A representation of the solutions involving integers is presented