What question did this study set out to answer?

The aim is to establish the Domb Apéry-limit and its relationship to the Ramanujan Machine conjecture.

April 5, 2026Open Access

The Domb Apéry-limit and a proof of the Ramanujan Machine conjecture Z2

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Research proves Domb Apéry-limit and reveals continued fraction identity for Apéry constant, suggesting important mathematical connections.

The aim is to establish the Domb Apéry-limit and its relationship to the Ramanujan Machine conjecture.
Deriving an Atkin–Lehner transformation law for the Eichler integral.
Extracting the connection constant from the derivative of the period polynomial at the CM fixed point.
Establishing a continued fraction identity for the Apéry constant.
The Domb Apéry-limit is proven, resolving an open question since 2008.
A continued fraction identity for the Apéry constant is verified, linked to the Ramanujan Machine project.

Alex Shvets (2026) studied this question.

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Research proves Domb Apéry-limit and reveals continued fraction identity for Apéry constant, suggesting important mathematical connections.