Computational Discovery of a New Ramanujan-Type Series for 1/π² via PSLQ and Automated Certificate

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.