Periodic Continued Fractions
A regular periodic continued fraction consists of a finite initial block of partial denominators followed by a repeating block; if
then ΞΆ is a quadratic irrational number, and its representation as a regular continued fraction is periodic. Clearly any regular periodic continued fraction consists of restricted partial quotients, since none of the partial denominators can be greater than the largest of a0 through ak+m. Historically, mathematicians studied periodic continued fractions before considering the more general concept of restricted partial quotients.
Read more about this topic: Restricted Partial Quotients
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