An expansion of zeta(3) in continued fraction with parameter

TL;DR

This paper introduces a parametrized continued fraction expansion for Zeta(3) based on a family of points on the projective line, excluding a countable set of exceptional points.

Contribution

It extends the continued fraction representation of Zeta(3) by incorporating a parameterized family of points on the projective line, identifying the exceptional set.

Findings

Parameterized continued fraction for Zeta(3) derived

Exceptional set of points explicitly characterized

Framework for further generalizations suggested

Abstract

We present here continued fraction for Zeta(3) parametrized by some family of points (F,G) on projective line. This family of points can be obtained if from full projective line would be removed some no more than countable exeptional set of finite points. A countable set, which contains the above exeptional set of finite points, is specified also.