How to solve recurrence relations by the generalized hypergeometric series

Question

I am reading methods of solving recurrence relation on Wikipedia. There is one method:

Many linear homogeneous recurrence relations may be solved by means of the generalized hypergeometric series. Special cases of these lead to recurrence relations for the orthogonal polynomials, and many special functions. For example, the solution to $$J_{n+1}=\frac{2n}{z}J_n-J_{n-1}$$ is given by $$J_n=J_n(z), \,$$ the Bessel function.

There are no description regarding how to use the method of "generalized hypergeometric series", nor can I find some on the article for generalized hypergeometric series or on Bessel function. I was wondering if someone here can explain somehow or gives some references about that? Thanks and regards!

Answer 1

See the (on-line, downloadable) book

A = B, by Petkovsek, Wilf, and Zeilberger

It gives all sorts of links between hypergeometric series and recurrence relations.