On Catalan Constant Continued Fractions

TL;DR

This paper explores the generation of infinitely many continued fraction representations for the Catalan constant using computational and mathematical methods, without providing formal proofs.

Contribution

It introduces a method to generate numerous conjectural continued fractions for the Catalan constant, expanding the known expressions.

Findings

Generated infinitely many conjectural continued fractions for G

Used computational tools and mathematical derivations

No formal proofs provided for the conjectures

Abstract

The Ramanujan Machine project detects new expressions related to constants of interest, such as $\zeta$ function values, $\gamma$ and algebraic numbers (to name a few). In particular the project lists a number of conjectures concerning the Catalan constant $G= 0.91596559\ldots$ We show how to generate infinitely many. We used an ad hoc software toolchain and rather tedious mathematical developments. Because we do not provide a proper peer-reviewed proof of the relations given here we do not claim them to be theorems.