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What is the form of the following recursion relation? 
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#1
Dec2112, 02:06 PM

P: 273

Hi all, I have a recursion relation I am trying to solve:
[itex]{X_n} = \frac{1}{{1  {\alpha _0} \cdot {X_{n  1}}}} \to {X_n} = ?[/itex] What is the "mathematical form" of this recursionrelation? E.g., I know what a homogeneous, linear recursionrelation with constant coefficients looks like, and how to solve it; same with an inhomogeneous recursion relation. But what about this one? (alpha0 = a constant). All I know is that it looks like the closedform solution to the infinite geometric sum, and I don't know where to go from there. If someone tells me what the mathematical form of this is, I can Google examplesolutions that I can work off of, and/or see what a textbook says. bjn 


#2
Dec2212, 06:00 AM

P: 761

Hi !
In attachment, you can see the method (not the whole calculus) which leads to the closed form. 


#3
Dec2212, 07:28 AM

P: 273

Thanks, JJaquelin. As it turns out, I found a book on differenceequations, in which there is a topic on continued fractions, which is a less mainstream topic than differential equations, so I am reading that now.
FYI: the book is Elaydi Saber's book: "An Introduction to Difference Equations". 


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