Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Transformations and Associated Harmonic Expansions

Abstract

We provide an explicit analytical evaluation of the known rational Ramanujan-type series for the theory of signature 2. Focusing on the singular moduli $k_r$ for $r\in \{2,3,4,7\}$, we demonstrate that the underlying elliptic identities can be established through modular transformations of degree 2. In particular, we showcase a family of rational harmonic Ramanujan-type series for $1/\pi$ involving higher-degree polynomials

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