what is the "form" of the following recursion relation?

by bjnartowt
Tags: form, recursion, relation
bjnartowt is offline
Dec21-12, 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 recursion-relation? E.g., I know what a homogeneous, linear recursion-relation 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 closed-form 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 example-solutions that I can work off of, and/or see what a textbook says.

Phys.Org News Partner Science news on Phys.org
Lemurs match scent of a friend to sound of her voice
Repeated self-healing now possible in composite materials
'Heartbleed' fix may slow Web performance
JJacquelin is offline
Dec22-12, 06:00 AM
P: 744
Hi !

In attachment, you can see the method (not the whole calculus) which leads to the closed form.
Attached Thumbnails
Continuous Fraction.JPG  
bjnartowt is offline
Dec22-12, 07:28 AM
P: 273
Thanks, JJaquelin. As it turns out, I found a book on difference-equations, 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".

Register to reply

Related Discussions
In binary can we have a value with "deci" "centi" "mili" or more lower valued prefix? Computers 14
Recursion to print a "fractal pattern" Engineering, Comp Sci, & Technology Homework 3
What exactly allows a "differential relation" form of an equation? General Math 1
relation between "commutation" and "quantization" Quantum Physics 3
What's the actual difference between "undefined" and "indeterminate form"? Calculus 4