ABSTRACT
Applications and further properties of the Airy integral are given in Chapter 11. This chapter also introduces other solutions of (8.05). Ex. 8.1 Show that w = Aia(z) satisfies w" - 4zw' - 2w =O.
9 The Bessel Function J,(z)
9.1 For integer values of n and real or complex values of z, the function J,(z) is defined by Bessel's integral
The variables n and z are called respectively the order and argument of Jn (2). Theorem 1.1 shows that Jn(z) is an entire function of z. To facilitate the evaluation of its Maclaurin coefficients we first construct a representation by a contour integral. Equation (9.01) may be rewritten
$9 The Bessel Function J,(z)
Integration of the last term by parts produces
Equation (9.08) is Bessel's equation. It is of great importance in many physical problems.
