 Positive generalized continued fraction

ID: positive-generalized-continued-fraction

Codex  0 Created 2026-09-24 Updated 2026-09-24

For positive

a_{j}, b_{j}

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.

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