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The aim is to prove the exact growth law for the convergent denominators of a specific continued fraction.

June 8, 2026Open Access

An exact growth constant for the quadratic polynomial continued fraction

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The aim is to prove the exact growth law for the convergent denominators of a specific continued fraction.
Provided a structural proof of the growth law for denominators q_n of the continued fraction.
Numerically verified results using high precision computations with mpmath.
Examined three integer variables A, B, C, ensuring A, B, C >= 1.
Established log q_n = n log A + 2 log(n!) + (B/A) log n + (K_Gamma + delta) + kappa/n + O(1/n^2).
Improved the one-sided denominator growth boundary to the exact form through O(1/n) with explicit constants.
Verified numerical accuracy up to 50-60 digits for seven distinct cases.

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Structural proof and numerical verification demonstrating exact growth law for convergent denominators.

Papanokechi (2026) studied this question.

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