Can Continued Fractions be Evaluated?

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Homework Help Overview

The discussion revolves around the evaluation of a specific continued fraction expressed in both infix and postfix notation. The subject area pertains to mathematical analysis, particularly the properties and evaluations of continued fractions.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants express uncertainty about evaluating the continued fraction, with some suggesting looking up known results. Questions arise regarding the nature of the fraction and its classification as a simple continued fraction. There is also a discussion about the challenges of evaluating arbitrary continued fractions.

Discussion Status

The discussion is ongoing, with various perspectives shared. Some participants have attempted to clarify the nature of the problem and express curiosity about its evaluation. There is no explicit consensus on the evaluation, but there is an acknowledgment of the complexity involved.

Contextual Notes

Participants mention the convergence of the continued fraction to a specific value and reference external resources, indicating a mix of assumptions and interpretations regarding the problem's classification and evaluation.

csprof2000
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If anybody can evaluate this, please let me know...

Infix notation:
1/(2+3/(4+5/(6+7/(8+9/(10+11/(...))))))

Postfix notation:
1 2 3 4 5 6 ... n ... / + / + / + / + ... / + ...
 
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I can't evaluate it but I can look it up. It's BesselI(0,2)/BesselI(1,2). The inverse of Sloane A052119. http://www.research.att.com/~njas/sequences/A052119
 
Last edited by a moderator:
Dick said:
I can't evaluate it but I can look it up. It's BesselI(0,2)/BesselI(1,2). The inverse of Sloane A052119. http://www.research.att.com/~njas/sequences/A052119

Ooops. I was reading it as a simple continued fraction, and it's not, sorry.
 
Last edited by a moderator:
Why was this moved to homework help? This is no homework problem. I challenge whoever dared move this to this forum to provide the answer or relinquish their moderation powers. Silly mods.
 
The mods are just trying to make this a livable place. Sometimes they make mistakes. A moderator that makes occasional mistakes in relocating threads is a lot better than no moderation. Trust me. But anyway, do you have a good reason for thinking there is an evaluation and why do you want to know? Just curious.
 
If you like, one of those "silly mods" could just delete this for you.
 
Whoa guys, no offense meant. Sheesh, serious mods.

Anywho, the reason I was wondering about this was that a student asked about it in my class. Apparently this thing does converge to around ~0.38, and I was just wondering if a more "pure" mathematician could help me out.
 
If you think about it, it would be just as hard to 'evaluate' (express in terms of elementary functions) an arbitrary continued fraction as an arbitrary string of digits. About all you can do is see if somebody has stumbled across it somehow. I took 1+1/(2+1/(3+1/(4+1/(5+1/... and evaluated it to a reasonable number of significant digits and hunted for it in Sloane's list. Was pretty happy to find something until I realized I'd gotten your fraction wrong. I don't find a hit for your form.
 

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