Generalized Continued Fraction
A generalized continued fraction is an expression of the form
where the an (n > 0) are the partial numerators, the bn are the partial denominators, and the leading term b0 is called the integer part of the continued fraction.
To illustrate the use of generalized continued fractions, consider the following example. The sequence of partial denominators of the simple continued fraction of π does not show any obvious pattern:
or
However, several generalized continued fractions for π have a perfectly regular structure, such as:
The first two of these are special cases of the arctangent function with = 4 arctan 1.
Read more about this topic: Continued Fraction
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