Ramanujan-Sato-like series

Using the theory of Calabi-Yau differential equations we obtain all the parameters of Ramanujan-Sato-like series for $1/\pi^2$ as $q$-functions valid in the complex plane. Then we use these q-functions together with a conjecture to find new examples of series of non-hypergeometric type. To motivate our theory we begin with the simpler case of Ramanujan-Sato series for $1/\pi$.