Computational Discovery of a New Ramanujan-Type Series for 1/π² via PSLQ and Automated Certificate
Year: 2026
Type: preprint
Abstract: Title: Computational Discovery of a New Ramanujan-Type Series for 1/π² via PSLQ and Automated CertificateAuthor: Zhilei Chen (Guangdong Peizheng College, Guangzhou, China) This note reports the computational discovery of a new series expansion for 1/π², extending the class of Ramanujan-type formulas beyond the previously known cases involving the central binomial coefficient squared (the s=1/2 family). By employing an automated parameter-space search using the LLL-based PSLQ algorithm combined with high-precision numerical evaluation, we identified a new hypergeometric structure characterized by parameters (1/4, 1/6) yielding the value 256√3/π². Furthermore, we applied Creative Telescoping within the Ore algebra framework to automatically derive the fifth-order linear differential equation satisfied by the generating function of this series, along with its full certificate. While the final constant identification relies on modular form theory (Humbert surfaces), our results provide strong computational evidence and a complete algorithmic verification framework. This approach demonstrates the effectiveness of combining symbolic computation (PSLQ + CT) with high-precision arithmetic for discovering new mathematical identities.
Author: Chen, Zhilei
Institution: Guangdong Peizheng College
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203645945
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