Level $17$ Ramanujan-Sato series
Abstract
Two level 17 modular functions $$ r=q^{2}\prod_{n=1}^{\infty}(1-q^{n})^{\left(\frac{n}{17}\right)},\quad s=q^{2}\prod_{n=1}^{\infty}\frac{(1-q^{17n})^{3}}{(1-q^{n})^{3}}, $$ are used to construct a new class of Ramanujan-Sato series for $1/\pi$. The expansions are induced by modular identities similar to those level of 5 and 13 appearing in Ramanujan's Notebooks. A complete list of rational and quadratic series corresponding to singular values of the parameters is derived.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.00459
- arXiv:
- arXiv:1711.00459
- Bibcode:
- 2017arXiv171100459H
- Keywords:
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- Mathematics - Number Theory;
- 11F03;
- 11F11
- E-Print:
- 15 pages