Level $17$ Ramanujan-Sato series

Abstract

Two level 17 modular functions $$r=q^2\prod _{n=1}^{\infty }(1-q^n{)}^{\left(\frac{n}{17}\right)},s=q^2\prod _{n=1}^{\infty }\frac{(1-q^{17n}{)}^3}{(1-q^n{)}^3},$$ 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.

15 pages