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Positive generalized continued fraction

For positive

a_{j}, b_{j}

, define

p_{0} = a_{0}

,

p_{- 1} = 1

,

q_{0} = 1

,

q_{- 1} = 0

and

p_{j} = a_{j} p_{j - 1} + b_{j - 1} p_{j - 2}, q_{j} = a_{j} q_{j - 1} + b_{j - 1} q_{j - 2} .

Then

(p_{n} q_{n} b_{n} p_{n - 1} b_{n} q_{n - 1}) = \prod_{j = 0}^{n} (a_{j} 1 b_{j} 0),

and

p_{n} / q_{n}

is the corresponding finite generalized continued fraction.

Table of contents 101 2
- Convergence of a positive simple continued fraction Positive generalized continued fraction 72 1
  - All-one continued fraction and Fibonacci ratios Convergence of a positive simple continued fraction 32

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