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The Chudnovsky series is the rapidly converging identityThe absolute ratio of successive summands tends to $1728/640320^3$, approximately $6.58\times 10^{-15}$, giving about fourteen new decimal digits per term asymptotically. Keeping only $k=0$ gives $\pi \approx 640320^{3/2}/(12\cdot 13591409)$. The factorial ratio, not a direct geometric approximation of a circle, controls the numerical convergence.^[ref]

Yue Zhao authored a 2018 exposition outlining a modular proof of the Ramanujan–Chudnovsky identity for $1/\pi$. The original preprint verifies this exact name; it does not justify identifying the author with another similarly named mathematician.^[ref]

The Chudnovsky series is useful for high-precision calculation because successive terms shrink rapidly. A modular derivation connects such an efficient numerical identity with modular forms and elliptic-function theory, explaining why the constants are mathematically structured rather than arbitrary numerical coincidences.^[ref]