Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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!

share|improve this question
Recurrence relations can be solved using generating functions. Maybe this is what you are looking for? –  Matt N. Mar 6 '11 at 22:27
hypergeometric series are also mentioned in Wilf's book which is freely available here: math.upenn.edu/~wilf/gfologyLinked2.pdf –  Matt N. Mar 6 '11 at 22:29
@Matt: Thanks! How to solve recurrence relations using generating functions? –  Tim Mar 6 '11 at 22:39
For an example (tower of hanoi) look here: math.stackexchange.com/questions/24984/… –  Matt N. Mar 7 '11 at 7:54

1 Answer 1

up vote 5 down vote accepted

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.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.