(Generating function for Jn) Just as there is a “generating function” for the Legendre pol...

(Generating function for Jn) Just as there is a “generating function” for the Legendre polynomials [see (9) in Section[4.4] there is one for the Bessel function . It can be show that

And the left hand side is called the generating function for the Jn’s

Equation (8.1) is useful for deriving various properties of the Jn’s. For example, taking of both sides, show that