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