https://scholars.lib.ntu.edu.tw/handle/123456789/626607
標題: | Ramanujan-type 1/pi-series from bimodular forms | 作者: | Wang, LQ YI-FAN YANG |
關鍵字: | Ramanujan 1/pi-series; Bimodular forms; Apery-like sequence; Hypergeometric series; CM-points; LEGENDRE POLYNOMIALS; MODULAR-FORMS; SERIES; EQUATIONS; IDENTITIES; FORMULAS; ANALOGS; NUMBERS; 1/PI | 公開日期: | 十一月-2022 | 出版社: | SPRINGER | 卷: | 59 | 期: | 3 | 起(迄)頁: | 831 | 來源出版物: | RAMANUJAN JOURNAL | 摘要: | We develop an approach to establish 1 / π-series from bimodular forms. Utilizing this approach, we obtain new families of 2-variable 1 / π-series associated to Zagier’s sporadic Apéry-like sequences. We first establish a general form of 1 / π-series involving constants related to the evaluation of modular forms at CM-points. Then we discuss situations when the series have rational terms. In addition, we discuss strategies for evaluating the constants involved and present a number of explicit 1 / π-series. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/626607 | ISSN: | 1382-4090 | DOI: | 10.1007/s11139-021-00532-6 |
顯示於: | 數學系 |
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