Generalization to plus Logarithmic Terms

Derive a generalized Meijer G-function identity for approximating + and determine whether Rivoal’s recurrences arise as a special case of the Conservative Matrix Field framework.

Background

The authors report numerical observations that evaluating the same construction at values other than one appears to approximate constants of the form +. They explicitly identify as unresolved both the corresponding generalization of the Meijer G-function identity and the relationship between the resulting CMF construction and Rivoal’s recurrences.

References

A natural future direction is to generalize the Meijer G-function identity accordingly and clarify whether Rivoal's recurrences arise as a special case of the CMF framework.

— An Infinite Family of Apéry-like Recurrences for Euler's Constant  (2610.13919 - Kalisch et al., 9 Oct 2026) in Section 9, “Future Work,” item 1