Talk:Recurrence relation

This page may be a stub but still, it is excellent and covers the subject quite well. Keep up the good work.

Relationship to differential equations

This article should discuss the relationship between diference/recurrence equations and differential equations. Specifically, it should show that discretization of a diferential equation yields a difference equation. This relationship is of vital importance to numerical simulations of physical processes on computers. --Fredrik Orderud 01:17, 30 May 2005 (UTC)

Right. But I think that probably belongs at the bottom of the article, after the recurrence relation is defined. for now, I plan to comment out that section, does not look good to have an unfinished section in an otherwise nice article. Oleg Alexandrov 02:55, 30 May 2005 (UTC)

The part about the similarity between the method of solving recurrence equations and differential equations is rather sketchy. It should be either removed or rewritten. Karl Stroetmann 00:05:17, 1 October 2005 (CEST)

A more intuitive explanation?

In the main article, there is an introduction to solving linear recurrance relations:

"Consider, for example, a recurrence relation of the form

$a_{n}=Aa_{n-1}+Ba_{n-2}.\,$

Suppose that it has a solution of the form a_n = r^n."

About a year ago, someone (probably a student) asked "WHY?" in the actual body of the article, on the main page. Why assume this? I think the question is a good one with a useful answer.

The article already includes a mathematically rigorous explanation below this quote, but I believe that to be inaccessible to the less experienced students for whom this article would be most useful.

At minimum, I think that quote should include a note referencing the justification listed below.

Difference equations?

It is stated without justification that difference equations are "a specific type of recurrence relation." In what way are difference equations only a subset of recurrence relations? As far as I know, they are one and the same. If this is not the case, some explanation of how they differ is in order. Otherwise, my edit would be reasonable. --Roy W. Wright 21:57, 18 November 2006 (UTC)

The equation $a_{n+1}=\tan a_{n}\,$ is not called a difference equation, but it is a recurrence relation. -- Jitse Niesen (talk) 05:29, 19 November 2006 (UTC)

True, the definition given in many texts would exclude that relation. Then might it be appropriate to say in the article that a difference equation is a specific type of recurrence relation of the form $a_{n+1}=a_{n}+F(a_{n},...)\,$? -- Roy W. Wright 09:08, 23 November 2006 (UTC)

A simple recurrence with non constant coefficients

Can someone contribute an explicit solution to the recurrence

P(n+1) = n*[ P(n) + P(n-1) ] where P(0) = 1 & P(1) = 0.

P(n)/n! is among other things the probability that if n numbered balls are distributed randomly into n numbered pockets no ball will end up in the proper pocket. It is easy to see computationally that as n increases P(n)/n! tends toward 1/e.

22:21, 1 April 2007 (UTC) lklauder@wsof.com