TITLE: How to solve recurrence relations by the generalized hypergeometric series
QUESTION [5 upvotes]: 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!

REPLY [9 votes]: 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.